Question

Assume Cylinder A and Cone B are the same height and the bases have the same radius. If A has a volume of 18π cm3, what is the volume of B? (round to nearest whole number) A) 19 cm3 B) 21 cm3 C) 24 cm3 D) 36 cm3

Answer 1

Option A
`V_B=19\ cm^3`

Explanation:

The volume of a cone is:

`V_B = \pi(hr ^ 2)/(3)`

The volume of a cylinder is:

`V_A = \pi(r ^ 2)h`

Both figures have the same height h and the same radius r.

The volume of the cylinder
`V_A = 18\pi\ cm ^ 3`

We want to find the volume of the cone.

Then, we find r and h:

`V_A = 18\pi = \pi(r ^ 2)h`

We simplify.

`V_A = 18 = (r ^ 2)h`

Then the product of
`(r ^ 2)h = 18`.

We substitute this in the cone formula and get:

`V_B =(\pi)/(3)(18)\\\\V_B = (18)/(3)\pi\\\\V_B=19\ cm^3`

Answer 2

A) 19 cm3

Explanation:

Volume of a cone is calculated as:

`\text{Volume of cone}=(1)/(3)\pi r^(2)h`

Volume of a cylinder is calculated as:

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

From the above two expressions we can see that if the height and radius of a cone and cylinder will be equal, the volume of cone will be 1/3 of the volume of the cylinder.

We are given the volume of Cylinder A to be 18π. So the volume of Cone B will be:

Volume of Cone B = 1/3 of Volume of Cylinder A

Volume of cone B = 1/3 x 18π = 6π = 19 cm³ (rounded to nearest whole number)

Thus, the volume of given cone B will be 19 cm³ rounded of to nearest whole number.