volume of hemisphere whos area is 12.5 ft squared
Answers
Answer:
radius r = 1.41047396 m
base circumference C = 8.86226925 m
volume V = 5.87697483 m^3
curved surface area A = 12.5 m^2
base surface area B = 6.25 m^2
total surface area K = 18.75 m^2
In Terms of Pi πbase circumference C = 2.82094792 π m
volume V = 1.87069919 π m3
curved surface area A = 3.97887358 π m^2
base surface area B = 1.98943679 π m^2
total surface area K = 5.96831037 π m
Step-by-step explanation:
r = radiusC = base circumferenceV = volumeA = curved surface areaB = base surface areaK = total surface areaπ = pi = 3.1415926535898√ = square rootHemisphere Formulas in terms of radius r:Volume of a hemisphere:V = (2/3)πr^3
Circumference of the base of a hemisphere:C = 2πr
Curved surface area of a hemisphere (1 side, external only):A = 2πr^2
Calculate the base surface area of a hemisphere (a circle):B = πr^2
Total surface area of a hemisphere:K = (2πr^2) + (πr^2) = 3πr^2
Answer:
Approximately 6.4 ft³
Step-by-step explanation:
A *hemisphere* is half of a sphere. As far as surface area goes, we not only need to account for the curved area, but also the area of the circular disc at the bottom. The area of the curved region is going to be half the area of the whole sphere. Since a sphere with radius r has a surface area of 4πr², the curved part of the hemisphere must have half that, or 2πr². Add in the area of the circular disc, πr², and we have a total area of 3πr². Setting this equal to the given area of 12.5 ft², we can solve for r:
[tex]3\pi r^2=12.5\\r^2=12.5/3\pi\\\\r=\sqrt{12.5/3\pi}[/tex]
Now, using the formula for the volume of a sphere, [tex]V=(4/3)\pi r^3[/tex], we can substitute our new value for r and solve:
[tex]V=(4/3)\pi r^3\\=(4/3)\pi(\sqrt{12.5/3\pi})^3\\\approx 6.4[/tex]
Related Questions
Let (-4,-5) be the point on the terminal side of theta find cos (theta), sec (theta) & cot (theta)
Answers
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{-4}\\ b=\stackrel{opposite}{-5}\\ \end{cases} \\\\\\ c=\sqrt{(-4)^2 + (-5)^2}\implies c=\sqrt{41} \\\\[-0.35em] ~\dotfill[/tex]
[tex]cos(\theta )\implies \cfrac{\stackrel{adjacent}{-4}}{\underset{hypotenuse}{\sqrt{41}}}\implies \cfrac{-4}{\sqrt{41}}\cdot \cfrac{\sqrt{41}}{\sqrt{41}}\implies -\cfrac{4\sqrt{41}}{41} \\\\\\ sec(\theta )\cfrac{\stackrel{hypotenuse}{\sqrt{41}}}{\underset{adjacent}{-4}}\implies -\cfrac{\sqrt{41}}{4}~\hfill cot(\theta )\implies \cfrac{\stackrel{adjacent}{-4}}{\underset{opposite}{-5}}\implies \cfrac{4}{5}[/tex]
HELPPPPP I NEED HELP WITH MATH HOMEWORK
Answers
Answer:
The answer is B
Please read the explanation... it always helps!!!
Step-by-step explanation:
All of the choices ask for difference.... it really helps when you draw a number line to solve these types of questions....
but for B you will need to imagine a compass..
alrighty for option B lets examine why it is correct....
Imagine you were standing on a dot (lol)
you walked 1.5 steps to the left <--
then you walked 1.5 steps to the right -->
you can see that you walked in opposite directions and in the end you will be back where you started (aka on the dot, still lol)
meaning the displacement is zero
that is why option B is correct
i really hope this isn't confusing and it helps!!!
How do you find the frequency in statistics?
Answers
Answer:
Count the tally marks to determine the frequency of each class. The relative frequency of a data class is the percentage of data elements in that class. The relative frequency can be calculated using the formula fi=fn f i = f n , where f is the absolute frequency and n is the sum of all frequencies
Mina had a disco for her birthday. For every 2 boys at the disco, there were 3 girls. There were 35 children at the disco in total. How many boys were at the disco?
Answers
There were 14 boys at Mina's disco for her birthday.
What is a ratio?A ratio is a quantitative value that shows the number of times a certain value is in another value.
The number of boys at the disco can be calculated as shown below:It is given that for every 2 boys at the disco, there were 3 girls. This means that the ratio of boys to girls at the disco is 2:3.
Let the proportionality constant be x.
Therefore total boys and girls are 2x and 3x respectively.
There are 35 kids at the disco. This means that the number of boys plus girls is 35. It can be written as shown below:
2x + 3x = 35
⇒ x = 35/5
⇒ x = 7
Total number of boys = 2x
= 2 * 7
= 14 boys
Therefore the total number of boys at the disco is 14.
Learn more about ratios here: https://brainly.com/question/13513438
#SPJ2
What is the quotient? startfraction 2 y squared minus 6 y minus 20 over 4 y 12 endfraction divided by startfraction y squared 5 y 6 over 3 y squared 18 y 27 endfraction startfraction 2 over 3 (y minus 5) endfraction startfraction 3 (y minus 5) over 2 endfraction startfraction (y minus 5) (y 2) squared over 6 (y 3) squared endfraction startfraction 3 (y 5) (y minus 2) over 2 (y 2) endfraction
Answers
The quotient of two fractions, (2y² - 6y - 20)/(4y + 12) and (y² + 5y + 6)/(3y² + 18y + 27), is: 3(y - 5)/2
What is a Quotient?Quotient can be described as the result you get from dividing a term by another term.
Let's find the quotient of (2y² - 6y - 20)/(4y + 12) and (y² + 5y + 6)/(3y² + 18y + 27)
Quotient = (2y² - 6y - 20)/(4y + 12) ÷ (y² + 5y + 6)/(3y² + 18y + 27)
Change the division sign to multiplication sign and turn the second fraction upside down
(2y² - 6y - 20)/(4y + 12) × (3y² + 18y + 27)/(y² + 5y + 6)
Bringing out the common terms, we would have:
2(y² - 3y - 10)/4(y + 3) × 3(y² + 6y + 9)/(y² + 5y + 6)
Factorize
2(y - 5)(y + 2)/4(y + 3) × 3(y + 3)(y + 3)/(y + 3)(y + 2)
Cancel out common factors
= 3(y - 5)/2
Quotient = 3(y - 5)/2
Learn more about quotient on:
https://brainly.com/question/11418015
#SPJ4
Answer:b
Step-by-step explanation:
lol
i need some help with this question.
Answers
The scale factor will be 1.5. The corresponding angles are congruent because the size is changed not the angles.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
Adnan wants a larger garden.
He draws the triangle ΔPQR to show his original garden.
He wants to enlarge a garden, so he uses a dilation to form the image of the triangle ΔPQ'R'.
He uses vertex P as the center of the dilation.
The ratio of the corresponding sides will be given as
PQ'/PQ = Q'R'/QR = R'P/RP = 1.5
The scale factor will be 1.5.
The corresponding angles are congruent because the size is changed not the angles.
More about the dilation link is given below.
https://brainly.com/question/2856466
#SPJ1
The inside of a baking pan is to be lined with tinfoil. the pan is 12 inches long, 9 inches wide, and 1.5 inches tall. how many square inches of tinfoil are needed?
Answers
The inside of a baking pan is to be lined with tinfoil. Then the amount of tinfoil needed will be 171 square inches.
What is a rectangle?It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
The inside of a baking pan is to be lined with tinfoil. the pan is 12 inches long, 9 inches wide, and 1.5 inches tall.
Then the amount of the tinfoil will be
The surface area of the rectangle with an open lid is given as
Surface area = 2(LH + WH) + LW
Then the surface area of the tinfoil will be
Surface area = 2(12 x 1.5 + 9 x 1.5) + 12 x 9
Surface area = 2 (18 + 13.5) + 108
Surface area = 2 x 31.5 + 108
Surface area = 63 + 108
Surface area = 171 square inches
More about the rectangle link is given below.
https://brainly.com/question/10046743
#SPJ1
can someone please help me solve these math problems they are about triangle proofs
Answers
Answer:
Besides the givens:
12.
AC = EC, BC = DC; Definition of Midpoint
<ACB = <ECD; Vertical Angles Theorem
Triangle ABC = Triangle EDC; SAS Congruence Postulate
13.
AD = CD; Definition of Median
BD = BD; Reflexive Property
Triangle ABD = Triangle CBD; SSS Postulate
Step-by-step explanation:
None necessary.
What is 16 1/5 - 5 2/3?
Answers
Answer:
10.533
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Which is the correct solution to ‐3x<21?
Answers
this is because, when dividing an inequality by a negative number, you must flip the inequality sign
-3x < 21
x > -7
Answer:
Top right
Step-by-step explanation:
When mult/dividing by a negative number, the sign always flips.
Which expression has the greatest value?
(options are included in the image)
Answers
Answer:
(b) 16^(3/2)
Step-by-step explanation:
Your calculator is a good source of information about the values of numerical expressions.
__
Here, all of the expressions have a value of 16 except 16^(3/2). That has the greatest value.
_____
Additional comment
Assuming you're familiar with powers of 2 and the rules of exponents, you can evaluate these without a calculator:
∛(64²) = ∛(2^6)² = (2^12)^(1/3) = 2^4
16^(3/2) = (2^4)^(3/2) = 2^6 . . . . . has the greatest value
√(16²) = ((2^4)^2)^(1/2) = 2^(4·2/2) = 2^4
∛(8^4) = ((2^3)^4)^(1/3) = 2^(3·4/3) = 2^4
__
8= 2^3; 16 = 2^4; 64 = 2^6
(a^b)^c = a^(bc)
A root is equivalent to a fractional power. The cube root is the 1/3 power, for example.
what is the surface area of the sphere
Answers
Answer:The answer iis 1810.3cm^2
Step-by-step explanation:
Question :-
What is the surface area of the sphere that has a radius of 12 cm?Answer :-
The surface area of the sphere is 1809 cm².[tex] \rule{180pt}{3pt}[/tex]
Diagram :-
[tex]\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bold{12 \: cm}}\end{picture}[/tex]
Solution :-
As per the provided information in the given question, we have been given that the radius of the sphere is 12 cm. We have been asked to find or calculate the surface area of the sphere.
To calculate the surface area of the sphere, we will use the formula below :-
[tex]\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Sphere)} = 4\pi r^2 \:\:}}[/tex]
Substitute the given values into the above formula and solve for surface area:
[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4\pi r^2[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(3.14)(12 \: cm)^2[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(3.14)(144 \: cm^2)[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4)(452.16 \: cm^2)[/tex]
[tex]\sf:\implies \bold{Surface \: Area_{(Sphere)} = 1809 \: cm^2}[/tex]
Therefore :-
The surface area of the sphere is 1809 cm².[tex]\\[/tex]
Learn more about the surface area of the sphere at https://brainly.com/question/28988747
Have a great day! <33
Evaluate f(-2): f(x)=3/2x-4
Answers
Answer:
f(- 2) = - 7
Step-by-step explanation:
substitute x = - 2 into f(x)
f(- 2) = [tex]\frac{3}{2}[/tex] × - 2 - 4 = - 3 - 4 = - 7
Help me please I forgot how to do this
Answers
Which function rule is represented by the table?
y=4x-1
y=3x+2
y=2x+3
y=x+2
Answers
Answer:
[tex]y=2x+3[/tex]
Step-by-step explanation:
Sure hope this helps you
You have been given data about gas prices in 15 states.
2018 Gas Price Data
Max: $2.42
Min: $2.03
Mean: $2.098
Median: $2.06
Mode: $2.04
Variance: 0.0121
Standard Deviation: $0.1098
What does the range, standard deviation, and variance say about gas prices in 2018?
Answers
The range, standard deviation, and variance say about gas prices in 2018 discussed below
What is standard deviation and variance?Variance is the average squared deviations from the mean, while standard deviation is the square root of this number.
As the variance in 2018 is 0.0121.
A model with low variance means sampled data is close to where the model predicted it would be.
As the standard deviation in 2018 is 0.1098.
Low standard deviation means data are clustered around the mean
A small range means low variability in a distribution.
Learn more about standard deviation, variance here:
brainly.com/question/17084031
#SPJ1
Darci sets up a room for a banquet.
She has 54 chairs. She places 9 chairs
at each table. How many tables have
9 chairs?
Answers
Answer:
6 tables
Step-by-step explanation:
54 chairs divided by 9 chairs = 6 tables have 9 chairs :)
Answer:
Step-by-step explanation:
Given:
There are 54 chairs in total.She places 9 chairs at each table.To find:
Amount of tables that have 9 chairs.Solution:
⇒ 1 : Based on the given conditions, formulate
⇒ 54 ÷ 9
⇒ 2 : Calculate
54
----
9
= 6.75
Round down in this case, so
⇒ Answer: 6.
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
I believe that is the diameter.
Answer:
C. Diameter
Step-by-step explanation:
Circumference: The distance around the edge outside of the circle.
Diameter: The distance across the circle that goes through the center.
Radius: The distance halfway across the circle, which is half the diameter.
Center: The point or dot in the middle of a circle.
Carpet costs $8.30 per square foot. How much will it cost to carpet the room? Show your work.
The area is 812ft
Answers
Answer:
about 98 dollars to cover the whole room in carpet
Step-by-step explanation:
The Carpet costs $8.30 per square foot, so 812 ÷ 8.30 = 97 with remainder. Therefore 98 as a rounded total ✅
Use the exchange rate £1 = €1.11 to convert €222 into £.
Answers
Given right triangle abc with altitude bd drawn to hypotenuse
ac. if ad = 8 and dc = 32, what is the length of bd?
Answers
Use Pythagorus
What is the volume of a cone with a height of 10.5 inches and a radius of 8 inches? cone v = 1 3 bh 1. rewrite the formula for the base area: v = 1 3 πr2h 2. substitute the values into the formula: v = 1 3 π(82)(10.5) 3.evaluate the power: v = 1 3 π(64)(10.5) 4.simplify using multiplication: v = 1 3 π(672) the cone has a volume of pi inches cubed.
Answers
The volume of the cone that has a radius of 8 in. and a height of 10.5 in. is: 703.7 in.³
What is the Volume of a Cone?Volume = 1/3πr²h
Given the parameters:
Height (h) = 10.5 in.Radius (r) = 8 in.Volume of the cone = 1/3πr²h = 1/3π(8²)(10.5)
Volume of the cone = 1/3π(64)(10.5)
Volume of the cone = 703.7 in.³
Learn more about volume of a cone on:
https://brainly.com/question/13677400
#SPJ1
Answer:
224Pi inches cubed
Step-by-step explanation:
How many Pennies did she collect in total
Answers
Answer: 4
Step-by-step explanation:
A cosmetologist conducted a survey to see which color hair was most popular among her customers. She surveyed 160 people. The results are shown in this circle chart.
How many more customers chose brown than red?
24 customers
35 customers
40 customers
88 customers
Circle graph titled Hair Color showing colors by percentage. Sectors are labeled Brown, 40 percent. Red, 15 percent. Black, 25 percent. Blonde, 20 percent.
Answers
Answer:
40 customers
Step-by-step explanation:
40% brown,
25% black
20% blonde
15% red
100% = 160
(40* 160)/ 100
6400 / 100 = 64
40% = 64 customers
(15 * 160)/100
2400/100 = 24
15% = 24 customers
64 customers - 24 customers =40 customers.
I NEED THE ANSWER ASAP
Simplify √40
Select one:
a. 20
b. 4
c. 4√10
d. 2√10
Answers
Answer:
Option D. [tex]\sf 2\sqrt{10}[/tex]
Hoping to increase pizza sales on Tuesdays, a new pizza restaurant prints and disperses the following coupon through email and fliers in a neighborhood marketing magazine
After ten weeks of the coupon offer, the owner of the restaurant needs to decide if the restaurant should continue to run the same special or offer a new one. Use the data collected in the table to determine whether or not the coupon appears to be generating sales for the restaurant.
Week Total
Sales
1 $859
2 $1,176
3 $1,480
4 $1,365
5 $1,576
6 $1,498
7 $1,180
8 $1,964
9 $1,634
10 $1,580
Part A: don’t answer
Part B: Use the total sales for weeks 4 and 9 to write an equation for the line of best fit. In your final answer, include all of your calculations.
Part C: in terms of the slope of the equation for the line of best fit, explain whether or not you think the coupon is responsible for the restaurant's increase or decrease in pizza sales on Tuesdays. Use complete sentences in your answer.
Part D: Assuming that the pizza restaurant wishes to continue the coupon for an additional five weeks, use the equation for the line of best fit to predict the restaurant's sales for the Tuesday of the 15th week.
—
Answers
B) y = 53.8x + 1149.8
C) Total Sales increase from one week to the next by $53.8.
Therefore, it is true to say that the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.
D) The restaurant's sales for the Monday of the 15th week is expected to be $1956.8
What is equation of line?The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term.
B) As by scatter plot,
The total sales for week 4 is given as 1,365 while that of week 9 is 1,634.
Therefore, we shall determine the equation for the line of best fit using the points;
( 4, 1365) and ( 9, 1634)
The first step would be to determine the slope of this line;
slope = (1634 - 1365)/ (9 - 4)
= 53.8
The equation of the line in slope-intercept form is thus;
Sales = 53.8(Week) + c
We need to determine c, the y-intercept. We can use the point ( 4, 1365);
1365= 53.8(4) + c
c = 1365-215.2
c = 1149.8
The equation of the line of best fit is thus;
y = 53.8x + 1149.8
C) The slope of the equation for the lines of best fit was found to be 53.8.
This value is positive which implies
Total Sales increase from one week to the next by $53.8.
The slope in regression is defined as the change in y for every unit change in x.
Therefore, it is true to say that the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.
D) The equation for the line of best fit was found to be;
y = 53.8x+ 1149.8
where y denotes the total sales and x the corresponding week. We are required to determine y when x is 15;
y = 53.8(15) + 1149.8
y = 1956.8
Therefore, the restaurant's sales for the Monday of the 15th week is expected to be $1956.8.
Learn more about equation of line here:
https://brainly.com/question/21511618
#SPJ1
Find the
median of 3,
4, 4, 5, 5, 6,
7, and 7.
Answers
Answer:
Answer is 5
Step-by-step explanation:
Arrange the data in an ascending order and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.
If two supplementary angles are in the ratio of 7: 8 ,find them.
Answers
Answer:
84° and 96°Step-by-step explanation :
Given :
Two supplementary angles are in the ratio of 7: 8To Find :
The two anglesSolution :
Let the angles be 7x and 8x respectively
As We know that, Sum of supplementary angles is always 180°
So, Adding Both the angles,
→ 7x + 8x = 180°
→ 15x = 180°
→ x = 180/15
→ x = 12
Hence,
7x = 7(12) = 84° 8x = 8(12) = 96°Therefore,
The required angles are 84° and 96°the length of one base of a trapezoid is 19 meters and the length of the other base is 27 meters. find the length of the median.
Answers
Answer:
23 m
Step-by-step explanation:
the median is calculated as
half the sum of the parallel bases , then
median = [tex]\frac{19+27}{2}[/tex] = [tex]\frac{46}{2}[/tex] = 23
What is the perimeter of the parallelogram?
Answers
Answer:
2(a+b)
Step-by-step explanation:
