Question

Find the volume of the composite solid. Round your answer to the nearest hundredth.

The volume is about _____ cubic meters.
(5.1)

Answer 1

Volume of the cube

• Side³
• (5.1)³
• 132.65m³

For the cone

• Radius of base=r=5.1/2=2.55m
• Height=h=5.1m

Volume

• 1/3πr²h
• 1/3(π)(2.55)²(5.1)
• 34.71m³

Total volume of the figure

• 132.65-34.71
• 97.94m³

Answer 2

97.92 m³ (nearest hundredth)

Explanation:

The composite solid is a cube with a cone cut out.

Therefore, to find the volume of the solid, subtract the volume of the cone from the volume of the cube.

Volume of Cube

`\textsf{Volume of a cube}=\sf s^3 \quad\textsf{(where s is the side length)}`

Given:

• s = 5.1 m

Substitute given value into the formula:

`\begin{aligned}\implies \sf V_(cube) & = \sf 5.1^3\\& = \sf 132.651\: m^3\end{aligned}`

Volume of Cone

`\textsf{Volume of a cone}=\sf (1)/(3) \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}`

Given:

• 
  `\sf r=(1)/(2)(5.1)=2.55\:m`

• 
  `\sf h = 5.1\:m`

Substitute given values into the formula:

`\begin{aligned}\sf \implies V_(cone) & = \sf (1)/(3) \pi (2.55^2)(5.1)\\& = \sf 11.05425 \pi \: m^3\end{aligned}`

Volume of Composite Solid

`\begin{aligned}\sf V_(solid) & = \sf V_(cube)-V_(cone)\\& = \sf 132.651-11.05425 \pi \\& = \sf 97.92304941...\\& = \sf 97.92 \: m^3 \: (nearest\:hundredth)\end{aligned}`