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Question

The volumes of two spheres are in the ratio 64:27 and the sum of their radii is 7 cm. What is the difference in their total surface areas?

A
88 cm2
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B
100 cm2
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C
84 cm2
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D
44 cm2
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Solution

The correct option is A 88 cm2
Let r1 and r2 be the radii of two spheres, the ratio of volumes of which is 64 : 27.
i.e., 43πr3143πr32=6427
r31r32=4333
(r1r2)3=(43)³
r1r2=43

Since the sum of the radii is 7 cm, we should have r1=4 cm and r2=3 cm
Then, the difference between the surface areas of the two spheres is
= 4πr₁² - 4πr₂²
= 4π (r₁² - r₂²)
= 4π (4² - 3²)
= 4π (16-9)
= 4π (7)
= 4×227× 7
= 88 cm2

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