Question

a fishbowl shaped like a sphere is filled with water. The fishbowl has a diameter of 16 inches. Which measurement is closest to the volume of water in the fishbowl in cubic inches?

Answer 1

2,144.66 in³

Explanation:

∵ The volume of a sphere,

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

Where,

r = radius of the sphere,

If Diameter of a sphere = 16 inches,

Then the radius of the sphere, r =
`(16)/(2)` = 8 inches

So, the volume of the sphere,

`V=(4)/(3)\pi (8)^3`

`=(4)/(3)* 512`

`=2144.66058485`

`\approx 2144.66\text{ square inches }`

∵ the fishbowl shaped like a sphere having diameter 16 in is filled with water.

Thus, the volume of the water in the fish bowl = volume of sphere having diameter 16 inches

= 2,144.66 in³

Answer 2

The volume of the water in the fishbowl is equal to

`(682(2)/(3))\pi\ in^(3)` or
`2,144.6\ in^(3)`

Explanation:

we know that

The volume of the sphere (a fishbowl) is equal to

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

In this problem we have

`r=16/2=8\ in` ----> the radius is half the diameter

substitute

`V=(4)/(3)\pi (8^(3))=(2,048)/(3)\pi\ in^(3)`

convert to mixed number

`(2,048)/(3)\pi\ in^(3)=\pi ((2,046)/(3)+(2)/(3))=(682(2)/(3))\pi\ in^(3)`

`(3.14156)*(682(2)/(3))=2,144.6\ in^(3)`