The surface area of a sphere is (frac{792}{7} cm^2). Find, correct to the nearest whole number, its volume. [Take (pi = frac{22}{7})]
-
A.
113(cm^3) -
B.
131(cm^3) -
C.
311(cm^3) -
D.
414(cm^3)
Correct Answer: Option A
Explanation
Surface area of a sphere = (4 pi r^2)
(4 pi r^2) = (frac{792}{7}cm^2)
4 x (frac{22}{7}) x (r^2) = (frac{792}{7})
(r^2) = (frac{792}{7}) x (frac{7}{4 times 22})
= 9
r = (sqrt{9})
= 3cm
Hence, volume of sphere
= (frac{4}{3} pi r^3)
= (frac{4}{3} times frac{22}{7} times 3 times 3 times 3 )
= (frac{4 times 22 times 9}{7})
(approx) = 113.143
= 113(cm^3) (to the nearest whole number)