Question

A spherical fish bowl is half-filled with water. The center of the bowl is C, and the length of segment AB is 16 inches, as shown below. Use Twenty two over seven for pi.

A sphere with diameter 16 inches is drawn.

Which of the following can be used to calculate the volume of water inside the fish bowl?

1 over 24 over 322 over 7(82)(16)
1 over 24 over 322 over 7(83)
1 over 24 over 322 over 7(162)(8)
1 over 24 over 322 over 7(163)

Answer 1

B.
`(1)/(2)*(4)/(3)* (22)/(7)* 8^3`

Explanation:

We have been given that a fish bowl has a diameter of 16 inches. We are asked to find the half-volume of the water inside the fish bowl.

We will use volume of sphere formula to solve the given problem.

`\text{Volume of sphere}=(4)/(3)\pi r^3`, where r represents radius of sphere.

Let us figure out radius of fish bowl by dividing its diameter by 2 as:

`r=(16)/(2)=8`

`\text{Volume of half filled fish bowl}=(1)/(2)*(4)/(3)* (22)/(7)* r^3`

`\text{Volume of half filled fish bowl}=(1)/(2)*(4)/(3)* (22)/(7)* 8^3`

Therefore, option B is the correct choice.

Answer 2

The second choice

1 over
`2/4` over
`3/22` over
`7/(8^(3))`

Explanation:

we know that

The volume of a sphere is equal to

`V=(4)/(3)\pi r^(3)`

In this problem we have

`r=16/2=8\ in`

`\pi=22/7`

To find the volume of water calculate the volume of semi-sphere

so

`V=(1)/(2)(4)/(3)\pi r^(3)` ------> volume of semi-sphere

substitute the values

`V=(1)/(2)(4)/(3)((22)/(7))(8)^(3)`

1 over
`2/4` over
`3/22` over
`7/(8^(3))`