In the figure above, the bases of the right uniform solid are triangles with sides of length 5, 12, and 13. If the surface area of the solid is 360, what is the volume ?

Options

A. 30
B. 180
C. 300
D. 600

Answer

C

Explanation

The surface area is the sum of the areas of the faces. To find the areas of the faces, you need to figure out what kinds of polygons they are so that you'll know what formulas to use. Start with the bases, which are said to be ''triangles with sides of lengths 5, 12, and 13.'' If these side lengths don't ring a bell in your head, go back and study your Pythogorean triplets. This is a 5-12-13 triangle, which means it's a right triangle, which means that you can use the legs as the base and height to find the area :
Area of Right Triangle `=(1)/(2)("leg"_(1))("leg"_(2))=(1)/(2)(5)(12)=30`
That's the area of each of the bases. Now call the height of the solid h. The other three faces are rectangles with areas `5xxh, 12xxh`, and `13xxh`. The total surface area, then, is `30+30+5h+12h+13h=60+30h`.
Since the problem tells us that the surface area is 360,
`60+30h=360`
`h=10`
Volume = base `xx` height `= 30xx10=300`. The answer is (C ).