Question

The diagram shows a solid shape.

The volume of the cone is 270 cm.
Work out the volume of the solid shape.
Give your answer in terms of pi​

Answer 1

`756\pi`

Solution,

Volume of cone=270 pi cm^3

`(1)/(3) \pi \: {r}^(2) = 270\pi \\ or \: {r}^(2) * 10 = 270 * 3 \\ or \: {r}^(2) * 10 = 810 \\ or \: {r}^(2) = (810)/(10) \\ or \: {r}^(2) = 81 \\ or \: r = √(81) \\ or \: r = \sqrt{ {9}^(2) } \\ r = 9 \: cm`

Volume of semisphere:

`(2)/(3) \pi {r}^(3) \\ = \: (2)/(3) * \pi * 9 * 9 * 9 \\ = 486\pi`

Total:

`270\pi + 486\pi \\ = 756\pi`

hope this helps...

Good luck on your assignment..