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Volume of a hollow sphere is $\frac{11352}{7} c m^{3}$ . If the outer radius is 8 cm, find the inner radius of the sphere. (Take π= $\frac{22}{7}$ )

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5 cm

8 cm

9 cm

3 cm

answer is A.

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Detailed Solution

Let's say that the inside radius of the hollow sphere is x cm and the outside radius is y=8 cm
Question Image

.
Using the formula V=

\frac{4}{3} π r^{3}

, the volume of the outside sphere is

\frac{4}{3} π 8^{3}

and the volume of the inside sphere is

\frac{4}{3} π x^{3}

.
The volume of the hollow sphere (shaded part) will be

\frac{4}{3} π 8^{3} - \frac{4}{3} π x^{3}

. .
According to the question:

\frac{4}{3} π 8^{3} - \frac{4}{3} π x^{3}

\frac{11352}{7}

Taking out the common factors

\frac{4}{3} π

and using π=

\frac{22}{7}

, we get:
⇒

\frac{4}{3}

\frac{22}{7}

×(

8^{3} - x^{3}

\frac{11352}{7}

⇒(

8^{3} - x^{3}

) =)=

\frac{11352}{7}

×)=

\frac{7}{22}

\frac{3}{4}

Note that 11352 is multiple of 11, because (1+3+2)−(1+5)=6−6=0. Dividing 11352 by 22 and cancelling out the 7's, we get:
⇒ 512−

x^{3}

=516×

\frac{3}{4}

⇒ 512−

x^{3}

=129×3
⇒ 512−

x^{3}

=387
⇒

x^{3}

=512−387
⇒

x^{3}

=125
Since, 5×5×5=125, we get:
⇒ x=5.
∴ The inner radius of the sphere is 5 cm.

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