Question

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Juan builds this pedestal for a trophy.

What is the volume of the pedestal?

Answer 1

112 in³

Explanation:

The pedestal is made up of two rectangular prisms.

`\boxed{\begin{minipage}{5.8 cm}\underline{Volume of a rectangular prism}\\\\$V=w\cdot l\cdot h$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width of the base. \\ \phantom{ww}$\bullet$ $l$ is the length of the base.\\\phantom{ww}$\bullet$ $h$ is the height of the prism.\\\end{minipage}}`

The dimensions of the largest rectangular prism are:

• w = 2 in
• l = 9 in
• h = 4 in

Therefore, the volume of the largest rectangular prism is:

`\begin{aligned}\implies V&=2 \cdot 9 \cdot 4\\&=18 \cdot 4\\&=72\;\rm in^3\end{aligned}`

The dimensions of the smaller rectangular prism are:

• w = 2 in
• l = 9 - 2 - 2 = 5 in
• h = 4 in

Therefore, the volume of the smaller rectangular prism is:

`\begin{aligned}\implies V&=2 \cdot 5 \cdot 4\\&=10\cdot 4\\&=40\;\rm in^3\end{aligned}`

The volume of the pedestal is the sum of the volumes of the largest and smaller rectangular prisms:

`\implies V=72+40=112\; \rm in^3`

Therefore, the volume of the pedestal is 112 in³.

Answer 2

• 112 in³

------------------------------------

The pedestal is the combination of two rectangular prisms.

One of them has dimensions:

• 9 in by 2 in by 4 in

Its volume is:

• V = 9*2*4 = 72 in³

The other one has dimensions:

• (9 - 2 - 2) = 5 in by 2 in by 4 in

Its volume is:

• V = 5*2*4 = 40 in³

Total volume is:

• 72 + 40 = 112 in³