Question

The total surface area of a hemisphere of diameter \( 14 \) cm is:

• A. \( 147\pi \) cm\(^2\)
• B. \( 198\pi \) cm\(^2\)
• C. \( 488\pi \) cm\(^2\)
• D. \( 396\pi \) cm\(^2\)

Hint:

For hemispheres, the total surface area is: \[ \text{TSA} = 3\pi r^2 \] and the curved surface area is: \[ \text{CSA} = 2\pi r^2 \]

Answer 1

The Correct Option is B

The total surface area (TSA) of a hemisphere is:
\[ \text{TSA} = 3\pi r^2 \] Given the diameter \( d = 14 \) cm, so radius:
\[ r = \frac{14}{2} = 7 \text{ cm} \] \[ \text{TSA} = 3\pi (7)^2 = 3\pi (49) = 147\pi \] Since the total surface area includes the circular base:
\[ \text{TSA} = 147\pi + 49\pi = 198\pi \text{ cm}^2 \]