Question

The whole surface area of a solid hemisphere of diameter \( \frac{1}{2} \) cm will be :

• A. \( \frac{1}{8} \pi \, \text{cm}^2 \)
• B. \( \frac{3}{16} \pi \, \text{cm}^2 \)
• C. \( \frac{1}{16} \pi \, \text{cm}^2 \)
• D. \( \frac{3}{32} \pi \, \text{cm}^2 \)

Hint:

The surface area of a solid hemisphere is given by \( 3 \pi r^2 \), where \( r \) is the radius of the hemisphere.

Answer 1

The Correct Option is C

The surface area of a hemisphere is given by: \[ \text{Surface Area} = 3 \pi r^2 \] The diameter of the hemisphere is \( \frac{1}{2} \) cm, so the radius \( r \) is: \[ r = \frac{1}{4} \, \text{cm} \] Now, substitute the value of \( r \) into the formula: \[ \text{Surface Area} = 3 \pi \left( \frac{1}{4} \right)^2 = 3 \pi \times \frac{1}{16} = \frac{3}{16} \pi \, \text{cm}^2 \] Thus, the whole surface area is \( \frac{3}{16} \pi \, \text{cm}^2 \).