Question

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

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

Hint:

For a hemisphere: - Curved surface area \( = 2\pi r^2 \) - Plane circular area \( = \pi r^2 \) Hence, total surface area \( = 3\pi r^2 \).

Answer 1

The Correct Option is B

Step 1: Formula for the total surface area of a solid hemisphere.
The whole surface area (TSA) of a solid hemisphere is given by: \[ \text{TSA} = 3\pi r^2 \] where \( r \) is the radius of the hemisphere.
Step 2: Substitute the given diameter.
Given diameter \( = \dfrac{1}{2} \, \text{cm} \), so \[ r = \dfrac{1}{4} \, \text{cm} \]
Step 3: Substitute in the formula.
\[ \text{TSA} = 3\pi \left(\dfrac{1}{4}\right)^2 = 3\pi \times \dfrac{1}{16} = \dfrac{3\pi}{16} \, \text{cm}^2 \]
Step 4: Final Answer.
\[ \boxed{\text{Whole surface area} = \dfrac{3}{16} \pi \, \text{cm}^2} \]