10. Two right prisms have similar bases. The first prism has height 5 and volume 100. A side on the base of the first prism has length 2, and the corresponding side on the base of the second prism has length 3. If the height of the second prism is 6, what is its volume?

First we calculate the base of the first one, remember the formula for volume is area of the base multiplied by the height, we know that the volume is 100 and the height is 5, so we divide volume by height and find that the base of the area is 20.

Now we know one side of the base, which is 2, if we divide 20 by 2, we know that the other side is 10.

We have similar bases so the rule 2:3 applies for the other side of the second prism:

[tex]\frac{2}{3} =\frac{10}{x} \\x=\frac{30}{2}=15[/tex]

So the other side of the second prism equals 15.

We just have to multiply to know the area of the base:

Area: Length x Width= 15x4=45

Volume= Area of the basex Height= 45x 6= 260

So the volume of the second prism is 260.