The surface area of a sphere is 1386 cm2. Its volume is

Question:

The surface area of a sphere is 1386 cm2. Its volume is
(a) 1617 cm3
(b) 3234 cm3
(c) 4851 cm3
(d) 9702 cm3

Solution:

(c) $4851 \mathrm{~cm}^{3}$

Surface area $=1386 \mathrm{~cm}^{2}$

Let r cm be the radius of the sphere.
Then we have:

$4 \pi r^{2}=1386$

$\Rightarrow r^{2}=\frac{1386 \times 7}{4 \times 22}=110.25$

$\Rightarrow r=10.5 \mathrm{~cm}$

$\therefore$ Volume of the sphere $=\frac{4}{3} \pi r^{3}$

$=\frac{4}{3} \times \frac{22}{7} \times 10.5 \times 10.5 \times 10.5$

$=4851 \mathrm{~cm}^{3}$

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