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Lynette has a metal doorstop with the dimensions shown. Each cubic centimeter of the metal in the doorstop has a mass of about 8.1 grams. Find the volume of the metal in the doorstop. Then find the mass of the doorstop, 10 cm 35 cm 8 am am? The volume of the metal is The mass of the doorstop is

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The doorstop has the shape of a triangular prism.

To compute the Volume of it, first, we need to find the area of the triangle located at the base.

The area of a triangle is calculated as follows:


A=\text{base}\cdot\text{height}\cdot(1)/(2)

From the picture, the base is 10 cm and the height is 8 cm, then:


\begin{gathered} A=10\cdot8\cdot(1)/(2) \\ A=40\operatorname{cm}^2 \end{gathered}

Now, we can compute the volume as follows:


\begin{gathered} V=\text{area of the triangle}\cdot\text{ height of the prism} \\ V=40\cdot3.5 \\ V=140\operatorname{cm}^3 \end{gathered}

1 cubic centimeter has a mass of 8.1 grams.

To find the mass of 140 cubic centimeters, we can use the next proportion:


\begin{gathered} \frac{1\operatorname{cm}}{140\operatorname{cm}^3}=\frac{8.1\text{ grams}}{x\text{ grams}} \\ 1\cdot x=8.1\cdot140 \\ x=1134\text{ grams} \end{gathered}

User Corey Burnett
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