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

The volume is about _____ cubic meters.
(5.1)

Find the volume of the composite solid. Round your answer to the nearest hundredth-example-1

2 Answers

10 votes

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
User Fabio Mora
by
7.6k points
7 votes

Answer:

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}

User OGreeni
by
8.0k points

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