Question

A hemispherical dome is constructed from 1cm thick metallic sheet, if the inner radius of the dome is 99cm, then find the volume of used metal sheet??

Answer 1

Inner radius of dome  r = 99 Cm
Outer radius of the Dome = 99 + 1
                                         = 100 Cm
Thus
Inner volume of dome = 2/3 pi r^3
                                    = 2/3 pi * 99^3
                                   = 2.03 m^3
Outer volume of Dome = 2/3 pi * R^3
                                    = 2/3 * 3.14 * 1
                                    = 2.09 m^3
Thus
volume of sheet = 2.09 - 2.03
                          = 0.06 m^3

Answer 2

Solution :-

Let r be the inner radius and R be the outer radius of the hemispherical dome.

Thickness of the metallic sheet = 1 cm

Inner Radius is 99 cm then the outer radius will be 99 cm + 1 cm = 100cm

Volume of the metallic sheet used = Outer volume of the dome - Inner volume of the dome

⇒ 2/3πr³ - 2/3πR³

⇒ 2/3*22/7*100*100*100 - 2/3*22/7*99*99*99

⇒ 44000000/21 - 42693156/21

⇒ 2095238.095 - 2033007.428

= 62230.667 cm³

So, volume of metallic sheet used is 62230.667 cm³

Answer.