Question

In the figure given below, a cylinder is inserted into a cone, and the vertical height of the cone is 30 cm. The diameter of the cylinder is 8 cm. What is the volume of the cone? The base of the cylinder and the base of the cone are on the same plane.

• A. \(3000\pi \text{ cm}^3\)
• B. \(4860\pi \text{ cm}^3\)
• C. \(2800\pi \text{ cm}^3\)
• D. Cannot be determined

Answer 1

The Correct Option is A

Step 1: Base half-angle \(=60^{\circ}\), so \(\tan60^{\circ}=\frac{30}{r}\), giving \(r=\frac{30}{\sqrt3}=10\sqrt3\) cm.
Step 2: Cone volume \(=\frac13\pi r^{2}h=\frac13\pi(300)(30)\).
Step 3: This gives \(3000\pi\text{ cm}^{3}\).
\[ \boxed{3000\pi \text{ cm}^3} \]