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A student has an L-shaped eraser as shown below with the dimensions given. If the factory that produces this eraser sells them in packs of 20, how many cubic millimeters of eraser material do they need to create each pack of eraser?

A student has an L-shaped eraser as shown below with the dimensions given. If the-example-1

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ANSWER


480,000\operatorname{mm}^3

Step-by-step explanation

We want to find the volume of 20 L-shaped erasers.

First, we have to find the volume of one eraser. To do this, we have to partition the eraser into two rectangular prisms:

To find the volume of the prism, apply the formula:


V=L\cdot W\cdot H

where L = length; W = width; H = height

Therefore, for A, we have:


\begin{gathered} V_A=60\cdot20\cdot10 \\ V_A=12,000\operatorname{mm}^3 \end{gathered}

And for B, we have:


\begin{gathered} V_B=60\cdot20\cdot10 \\ V_B=12,000\operatorname{mm}^3 \end{gathered}

The volume of the shape is the sum of the volumes of the partitions. Hence, the volume of the shape is:


\begin{gathered} V=V_A+V_B_{} \\ V=12,000+12,000 \\ V=24,000\operatorname{mm}^3 \end{gathered}

Hence, a pack of 20 will have a volume of:


\begin{gathered} V=20\cdot24,000 \\ V=480,000\operatorname{mm}^3 \end{gathered}

That is the amount of material needed to create each pack of erasers.

A student has an L-shaped eraser as shown below with the dimensions given. If the-example-1
User DrAl
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