UPSC CDS 2 2021 Math Paper

Given, density of metal of spherical shell =7g∕cm3
Internal radius, r1=3cm
External radius, r2=6cm
Volume of the hollow spherical shell
=‌

4

3

π(r23−r13)
=‌

4

3

×‌

22

7

×(63−33)
=‌

4

3

×‌

22

7

×(216−27)
=‌

88

21

×189
=88×9=792cm3
∵ Mass = Density × Volume
∴ Mass of the shell =7×792=5544g
Hence, mass of the shell is 5544g.