Question

The volume of a rectangular prism with a cone shaped hole in it is approximately 163.22cm³ (as shown below).

✏️ What is the height of the cone?

Answer 1

Height of the cone = 5 cm

Explanation:

Volume of the rectangular prism with a cone shaped hole = Volume of the rectangular prism - Volume of the cone

Volume of the rectangular prism = Length × Width × Height

= 5 × 5 × 7

= 175 cm³

Volume of the cone =
`(1)/(3)\pi r^(2)h`

Here, r = Radius of the cone

h = Height of the cone

Volume of the cone =
`(1)/(3)\pi ((3)/(2))^(2)(h)`

= 0.75πh cm³

Volume of the rectangular prism with a hole = 163.22 cm³

175 - 0.75πh = 163.22

0.75πh = 175 - 163.22

0.75πh = 11.78

h = 5 cm