Question

find the volume of a sphere whose surface area is 154cm^2

Answer 1

Surface area of sphere = 4 pi r^2

=> 154 = 4 × 22 × r^2 / 7

=> r^2 = 154 × 7 / 22 × 4

=> r^2 = 7 × 7 / 4

=> r = 7/2

Volume = 4/3 pi r^3

= 4 × 22 × 7 × 7 × 7 / 3 × 7 × 2 × 2 × 2

= 11 × 7 × 7 / 3

= 179.67 cm^3

Answer 2

Given,

Surface area of sphere is 154 cm^2

Surface area of sphere = 4πr^2

$4 \times \frac{22}{7} \times {r}^{2} = 154\\ {r}^{2} = \frac{154}{4} \times \frac{7}{22}\\{r}^{2} = \frac{49}{4} \\r = \sqrt{ \frac{49}{4} }\\r = \frac{7}{2}\\r= 3.5cm$

Volume of sphere = 4/3πr^3

$\frac{4}{3} \times \frac{22}{7} \times {3.5}^{3} \\ \frac{88}{21} \times 42.875 = 179.67 {cm}^{3}$

Therefore the volume of sphere is 179.67cm^3.