Question

if the radius of a cylinder is 2 cm and its height is 5 cm, what is its volume?
a. 15π cm³
b. 20π cm³
c. 10π cm³
d. 25π cm³

a cone has a height of 12 cm and a radius of 6 cm. what is its volume in terms of π?
a. 216π cm³
b. 144π cm³
c. 72π cm³
d. 288π cm³

Explanation:

Step1: Calculate the volume of the cylinder

The formula for the volume of a cylinder is \( V=\pi r^{2}h \). Given \( r = 2\ \text{cm} \) and \( h=5\ \text{cm} \), substitute into the formula: \( V=\pi\times(2)^{2}\times5=\pi\times4\times5 = 20\pi\ \text{cm}^3 \).

Step2: Calculate the volume of the cone

The formula for the volume of a cone is \( V=\frac{1}{3}\pi r^{2}h \). Given \( r = 6\ \text{cm} \) and \( h = 12\ \text{cm} \), substitute into the formula: \( V=\frac{1}{3}\pi\times(6)^{2}\times12=\frac{1}{3}\pi\times36\times12 = 144\pi\ \text{cm}^3 \).

Answer:

B. \( 20\pi\ \text{cm}^3 \)
A. \( 144\pi\ \text{cm}^3 \)