Question

a hollow spherical shell is made of metal of density 3 gram/cm³. If it's external and internal radii be 9 cm and 6cm,the weight of the shell(in kg)

Answer 1

Given, External radii R = 9 cm.

Given, Internal radii r = 6 cm.

We know that Volume of the spherical shell = (4/3) π(R³ - r³)

⇒ (4/3) * (22/7) * (9³ - 6³)

We know that a³ - b³ = (a + b)(a² + ab + b²)

⇒ (4/3) * (22/7) * (9 + 6)(9² + 72 + 6²)

⇒ (4/3) * (22/7) * (15) * (81 + 72 + 36)

⇒ (4/3) * (22/7) * (15) * (189)

⇒ (4) * (22/7) * (15) * 63

⇒ (4) * (22) * (15) * (9)

⇒ 11880 cm³.

Given that Density of metal = 3 gm/cm^3.

⇒ Weight of shell = 11880 * 3

                              = 35640 gm

                              = 35.64 kg.

Therefore, Weight of the shell = 35.64 kg.

Hope this helps!

Answer 2

Volume of metal=4/3pi(9^3-8^3)
~909 cm^3
Mass =density*volume
=4090.5 gram