Question : A hemispherical bowl is made of 1 cm thick steel. The inside radius of the bowl is 4 cm. The volume of the steel (in cm3) used in making the bowl is:
Option 1: $40\frac{2}{3}\pi$
Option 2: $27\frac{1}{3}\pi$
Option 3: $41\frac{1}{3}\pi$
Option 4: $35\frac{1}{3}\pi$
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Correct Answer: $40\frac{2}{3}\pi$
Solution :
Given: Inner radius $(r)$ = 4 cm
Outer radius $(R)$ = 4 + 1 = 5 cm
According to the question,
The volume of steel used
= $\frac{2}{3}×\pi (R^3-r^3)$
= $\frac{2}{3}×\pi (5^3-4^3)$
= $\frac{2}{3}×\pi (125-64)$
= $\frac{2}{3}×\pi ×61$
= $\frac{122}{3}×\pi$
= $40\frac{2}{3}\pi\ \text{cm}^3$
Hence, the correct answer is $40\frac{2}{3}\pi$.
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