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

Answer:

97.92 m³ (nearest hundredth)

Step-by-step 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

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

Given:

• $\sf r=\dfrac{1}{2}(5.1)=2.55\:m$

• $\sf h = 5.1\:m$

Substitute given values into the formula:

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

Volume of Composite Solid

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

Answer 2

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