Question

$\text{The volume of two spheres are in the ratio 64:27 and the sum of their radii is 7 cm.The difference in their total surface areas is}\left(a\right)38c{m}^2\left(b\right)58c{m}^2\left(c\right)78c{m}^2\left(d\right)88c{m}^2$

Answer 1

Ratio of volumes of two spheres = 64:27
((c) $\frac{4}{3}$ πr₁³)/((c) $\frac{4}{3}$ πr₂³) = (c) $\frac{64}{27}$
r₁³/r₂³ = 4³/3³
(r₁/r₂)³ = ((c) $\frac{4}{3}$)³
r₁/r₂ = (c) $\frac{4}{3}$

r₁ = 4 and r₂ = 3 as their sum is equal to 7.

Difference of their surface areas :
= 4πr₁² - 4πr₂²
= 4π (r₁² - r₂²)
= 4π (4² - 3²)
= 4π (16-9)
= 4π (7)
= 4((c) $\frac{22}{7}$) (7)
= 88 units

Ans-d