Question

The base diameter of a cone is \(10\) cm and its height is \(12\) cm. Then the volume of the cone is:

• A. \(400\pi\ \text{cm}^3\)
• B. \(300\pi\ \text{cm}^3\)
• C. \(100\pi\ \text{cm}^3\)
• D. \(200\pi\ \text{cm}^3\)

Hint:

Always halve the diameter to get the radius before using \(V=\frac{1}{3}\pi r^2 h\).

Answer 1

The Correct Option is C

Step 1: Write the volume formula of a cone.
\(V=\dfrac{1}{3}\pi r^2 h.\)
Step 2: Convert diameter to radius.
Diameter \(=10\) cm \(\Rightarrow\) radius \(r=\dfrac{10}{2}=5\) cm; height \(h=12\) cm.
Step 3: Substitute and compute.
\[ V=\frac{1}{3}\pi(5)^2(12)=\frac{1}{3}\pi\cdot25\cdot12 =\frac{300}{3}\pi=100\pi\ \text{cm}^3. \]
Step 4: Conclude.
Therefore, the volume is \(100\pi\ \text{cm}^3\).