The total surface area of a solid hemisphere is 1039.5 cm$^2$ . The volume(in cm$^3$) of the hemisphere is: (Take $\pi = \frac{22}{7}$)
Answer & explanation
Correct answer: option 3
We know that,
Total surface area of the hemisphere = 3πr2
Volume of the hemisphere = \(\frac{2}{3}\)πr3
We have,
Total surface area = 1039.5 cm2
Now, according to the question,
= 3πr2 = 1039.5
= 3 × \(\frac{22}{7}\) × r2 = 1039.5
= r2 = \(\frac{(1039.5 × 7)}{66}\) = 15.75 × 7 = 110.25
= r = \(\sqrt {110.25}\) = 10.5
Volume of the hemisphere = \(\frac{2}{3}\)× \(\frac{22}{7}\) × 10.5 × 10.5 × `10.5 = 2425.5