Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

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= $\frac{22}{7}$ )

a Right Circular Cone

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

5 cm

8 cm

9 cm

3 cm

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Get Expert Academic Guidance – Connect with a Counselor Today!