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3 years ago

8

Find the area of the circle. Round your answer to the nearest hundredth.

1 answer:

MissTica3 years ago

3 0

Answer:

176.63 cubic in. =A

Step-by-step explanation:

The area of a circle can be found by using the equation $\pi r^{2}$ =A. The problem gives us the diameter, but we need the radius. To find the radius divide the diameter by 2, so raduis= 7.5 in.

$\pi r^{2}$ =A

(3.14)( $7.5^{2}$ )=A

(3.14)(56.25)=A

176.63 cubic in. =A

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Answer:

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Step-by-step explanation:

GIVEN: A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of the dome is $84\text{ feet}$ , and the total height of the building up to the top of the dome is $91\text{ feet}$ .

TO FIND: what is the approximate total volume of the building.

SOLUTION:

let the height of the mountaintop be $h\text{ feet}$

As the dome hemispherical.

circumference of a hemisphere $=\frac{1}{2}\times2\pi\times radius$

$=\pi\times radius$

$\frac{22}{7}\times radius=84$

$radius=26.75\text{ feet}$

total height of the building up to the top of the dome $=\text{radius of hemisphere}+\text{height of mountaintop}$

$=26.75+h=91$

$h=64.25\text{ feet}$

Volume of building $=\text{volume of cylindrical mountaintop}+\text{volume of dome}$

$=\pi(radius)^2h+\frac{2}{3}\pi(radius)^3$

as radius of mountain top is same as dome

putting values

$=3.14(26.75)^264.75+\frac{2}{3}3.14(26.75)^3$

$=145484.6+40069.1$

$185553.7\text{ feet}^3$

Hence the total volume of the building is $185553.7\text{ feet}^3$

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Step-by-step explanation:

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