Question

The volume of a right circular cone is 300 cubic inches. What is the volume, in cubic inches, of a right cylinder th

Answer 1

Answer:

The volume of the cylinder is 900 cubic inches

Step-by-step explanation:

Given

Let V1 represent the volume of a cone and V2 represents the volume of a cylinder

$V_1 = 300in^3$

Required

Determine the volume of a cylinder with same dimension

The volume of a cone is calculated as:

$V_1 = \frac{1}{3}\pi r^2h$

The volume of a cylinder is calculated as:

$V_2 = \pi r^2h$

Since, the cone and cylinder have the same dimensions, we can substitute $\pi r^2h$ for $V_2$ in $V_1 = \frac{1}{3}\pi r^2h$

So, we have:

$V_1 = \frac{1}{3} * V_2$

Multiply both sides by 3

$3 * V_1 = \frac{1}{3} * V_2 * 3$

$3 * V_1 = V_2$

$V_2 = 3 * V_1$

Substitute $300in^3$ for $V_1$

$V_2 = 3 * 300in^3$

$V_2 = 900in^3$

Hence, the volume of the cylinder is 900 cubic inches