A solid right circular cone has a base radius of 7\text{ cm} and a height of 12\text{ cm}.… — JAMB UTME

A solid right circular cone has a base radius of $7\text{ cm}$ and a height of $12\text{ cm}$ . Taking $\pi = \frac{22}{7}$ , what is the volume of the cone?

$616\text{ cm}^3$ Answer
B
$1848\text{ cm}^3$
C
$924\text{ cm}^3$
D
$308\text{ cm}^3$

Answer

616\text{ cm}^3

The correct answer is obtained by applying the standard cone volume formula

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

. Substituting

r = 7

h = 12

, and

\pi = \frac{22}{7}

yields

V = 616\text{ cm}^3

Step-by-Step Solution

Identify the formula for the volume of a solid cone.

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

The volume of a cone is one-third the volume of a cylinder with the same base radius and height.

Substitute the given values into the formula.

V = \frac{1}{3} \times \frac{22}{7} \times (7)^2 \times 12

Given

r = 7\text{ cm}

h = 12\text{ cm}

, and

\pi = \frac{22}{7}

Simplify the expression to find the volume.

V = \frac{1}{3} \times \frac{22}{7} \times 49 \times 12 = 22 \times 7 \times 4 = 616\text{ cm}^3

Simplifying

\frac{49}{7} = 7

and

\frac{12}{3} = 4

leaves

22 \times 7 \times 4

Key Concept

Volume of a Right Circular Cone

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