Question

If the total surface area of a hemisphere is \(462\ \text{cm}^2\), then its diameter is:

• A. \(7\ \text{cm}\)
• B. \(14\ \text{cm}\)
• C. \(21\ \text{cm}\)
• D. \(22\ \text{cm}\)

Hint:

For a hemisphere, \(\text{TSA} = 2\pi r^2 + \pi r^2 = 3\pi r^2\). Once \(r\) is known, the diameter is simply \(2r\).

Answer 1

The Correct Option is B

Step 1: Use the total surface area (TSA) of a hemisphere.
TSA \(= 3\pi r^2\). Given \(3\pi r^2 = 462\).
Step 2: Solve for \(r\).
Taking \(\pi=\dfrac{22}{7}\):
\[ 3\cdot \frac{22}{7}\, r^2 = 462 \;\Rightarrow\; r^2 = \frac{462 \cdot 7}{66} = 49 \;\Rightarrow\; r = 7\ \text{cm}. \]
Step 3: Find the diameter.
Diameter \(= 2r = 2 \times 7 = 14\ \text{cm}.\)