Question

Lynette has a metal doorstop with the dimensions shown. Each cubic centimeter of the metal in the doorstop has a mass of about 8.6 grams. Find the volume of the metal in the doorstop. Then find the mass of the doorstop.

(Picture is provided)

Answer 1

75 is the volume. 510 is the mass.

Answer 2

The answers are:

Volume: 75 cubic centimeters

Mass: 645 grams

Explanation:

In order to determine both volume and mass of the doorstop, we have to know the formulas of a triangular prism.

I have attached an image that shows some formulas about triangular prism.

As we see in the image, a triangular prism consists basically in a triangular face and its projection.

So, using the variables and formula of the image:

B=10 cm

H=6 cm

L=2.5 cm

`V=(1)/(2)*B*H*L\\V=(1)/(2)*10*6*2.5\\V=75`

Then, we know the density of the metal that is:

δ=
`8.6 (gr)/(cm^3)`

So, the mass of the doorstop is:

m=δ*V

m=8.6
`(gr)/(cm^3)` * 75
`cm^3`

m=645 gr

Finally, the volume is 75
`cm^3` and the mass 645 gr