Question

Surface areas of two spheres are in the ratio 36:25
(a) Find the ratio of their volume
(b) If difference of the radii if 4cm, find the radius of each sphere.

Answer 1

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Answer 2

Dear Student,

● Answer -

(a) V1/V2 = 216/125

(b) r1 = 24 cm and r2 = 20 cm

● Explanation -

Let r1 and r2 be radii of spheres.

A1/A2 = 4πr1^2 / 4πr2^2

36/25 = r1^2 / r2^2

r1/r2 = 6/5

Given that r1 = r2 + 4,

(r2+4)/r2 = 6/5

5r2 + 20 = 6r2

r2 = 20 cm

So now,

r1 = r2 + 4

r1 = 20 + 4

r1 = 24 cm

Ratio of volumes is -

V1/V2 = (4/3 πr1^3) / (4/3 πr2^3)

V1/V2 = r1^3 / r2^3

V1/V2 = (6/5)^3

V1/V2 = 216/125

Thanks dear. Hope this helps you...