Question

The total surface area of a solid hemisphere of diameter ‘2d’ is :

• A. \(3\pi d^2\)
• B. \(2\pi d^2\)
• C. \(\frac{1}{2}\pi d^2\)
• D. \(\frac{3}{4}\pi d^2\)

Hint:

Don't confuse Total Surface Area (\(3\pi r^2\)) with Curved Surface Area (\(2\pi r^2\)). For a solid hemisphere, the base area \(\pi r^2\) must be included.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A solid hemisphere has two surfaces: a curved surface and a flat circular base. The Total Surface Area (TSA) is the sum of these two areas.
Step 2: Key Formula or Approach:
1. Radius \(r = \frac{\text{Diameter}}{2}\)
2. \(TSA = 3\pi r^2\)
Step 3: Detailed Explanation:
1. Given the diameter is \(2d\). 2. Calculate the radius: \[ r = \frac{2d}{2} = d \] 3. Substitute the radius into the TSA formula: \[ TSA = 3\pi(d)^2 \] \[ TSA = 3\pi d^2 \]
Step 4: Final Answer:
The total surface area is \(3\pi d^2\).