Question

The volume of a cylinder is 32.25 cubic inches. If a cone has the same height and radius as the cylinder, what is its volume?

8.06 cu. in.

10.75 cu. in.

21.5 cu. in.

32.25 cu. in.

Answer 1

option 2nd is correct

volume of a cone is, 10.75 cubic inches

Explanation:

Volume of a cone (V) is given by:

`V = (1)/(3) \pi r^2h` ......[1]

where,

r is the radius of the cone and h is the height of the cone respectively.

As per the statement:

The volume of a cylinder is 32.25 cubic inches.

Volume of a cylinder is given by:

`\text{Volume of a cylinder} = \pi r^2h`

⇒
`32.25 = 3.14 \cdot r^2h`

Divide both side by 3.14 we have;

`10.27 =(r')^2(h')`

`r</p><p>o(r')^2(h)= 10.27`

It is also given that a cone has the same height and radius as the cylinder.

⇒
`r' = r` and
`h' = h`

⇒
`r^2h = 10.27`

Using formula [1] we have;

`V = (1)/(3) \cdot 3.14 \cdot 10.27`

Simplify:

`V = 10.75` cubic inches

therefore, volume of a cone is, 10.75 cubic inches

Answer 2

10.75 cu.in., as volume of a cylinder is 3 times bigger than volume of a cone, according to their equations:

`V_(cylinder) = \pi^(2) rh V_(cone) = (1)/(3) \pi^(2) rh`