Question

if the edges of the base of a rectangular prism are 8 cm and 6 cm, and the diagonal is 10√2, what is the volume of the solid?

Answer 1

221.12 cm^3

Explanation:

Imagine that you have the 6cm side of the prism base facing you, and that you cut the prism in half through the vertex. Doing this will form two triangles. The hypotenuse of the triangle is the same as the "diagonal" that is 10√2 cm. The base of this triangle is half of the 6" side, or 3 cm.

Use the Pythagorean Theorem to determine the height (h) of the prism:

h^2 + 3^2 = (10√2)^2, or

h^2 = 200-9 = 191

Then the height is √191 cm

and the base area is 6cm times 8 cm, or 48 cm^2

and so we end up with the volume V = (1/3)(base area)(height), or

V = (1/3)(48 cm^2)(√191 cm), or

roughly 221.12 cm^3