22.7k views
23 votes
Solve both Question related to Volume of Solids. 50 Points​

Solve both Question related to Volume of Solids. 50 Points​-example-1
User WayneZhao
by
6.6k points

1 Answer

7 votes

Given for the cone:

  • base radius: 3a
  • perpendicular height: 4a

given for the spheres:

  • radius: a

Find volume of cone:


\sf \hookrightarrow (1)/(3) \pi r^2h


\sf \hookrightarrow (1)/(3) \pi (3a)^2(4a)


\sf \hookrightarrow 12\pi a^3

Find volume of sphere:


\sf \hookrightarrow (4)/(3) \pi r^3


\sf \hookrightarrow (4)/(3) \pi a^3

Divide volume of cone by volume of sphere:


\sf \hookrightarrow (12\pi a^3)/( (4)/(3) \pi a^3)


\rightarrow 9

Therefore proved 9 such spheres can be made using the metal cone.

We know that volume of cone is
12\pi a^3


\sf \rightarrow 12\pi a^3 = 12936


\sf \rightarrow a^3 = (12936)/(12\pi)


\sf \rightarrow a = \sqrt[3]{(12936)/(12\pi)}


\sf \rightarrow a =7

Therefore the radius of sphere is 7 cm

User Galeop
by
6.4k points