Question : A hemisphere has a 42 cm diameter. Find its curved surface area and the total surface area.
Option 1: 2772 cm2 and 4158 cm2
Option 2: 3772 cm2 and 5158 cm2
Option 3: 4770 cm2 and 4238 cm2
Option 4: 3072 cm2 and 4058 cm2
Correct Answer: 2772 cm 2 and 4158 cm 2
Solution :
Let the radius of the hemisphere be $r$.
Given, its diameter, $2r=42⇒r=21$
$\therefore$ The curved surface area of a hemisphere $= 2\pi r^2=2×\frac{22}{7}×21^2=2772\ \text{cm}^2$
$\therefore$ The total surface area of a hemisphere $= 3\pi r^2=3×\frac{22}{7}×21^2=4158\ \text{cm}^2$
Hence, the correct answers are 2772 cm
2
and 4158 cm
2
.
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