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 a hemisphere, the curved surface area is given by \( 2\pi r^2 \), while the total surface area includes the circular base and is given by \( 3\pi r^2 \).

Answer 1

The Correct Option is A

Step 1: Identify given values The diameter of the hemisphere is given as: \[ d = 14 \text{ cm} \] The radius is: \[ r = \frac{d}{2} = \frac{14}{2} = 7 \text{ cm} \] Step 2: Apply the formula for total surface area The total surface area of a hemisphere is given by: \[ A = 3\pi r^2 \] Substituting \( r = 7 \): \[ A = 3\pi (7)^2 \] \[ = 3\pi (49) \] \[ = 147\pi \, cm^2 \] Step 3: Conclusion Thus, the correct answer is: \[ 147 \pi \, cm^2 \]