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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?

The volume of a rectangular prism with a cone shaped hole in it is approximately 163.22cm-example-1
User Stephen Swensen
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1 Answer

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21 votes

Answer:

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

User Amila Isura
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