What is the volume of a frustum of a right pyramid with the area of the lower base equal to 100 square inches, the area of the upper base equal to 25 square inches, and the altitude equal to 12 inches?
a. 560 in^3
b. 700 in^3
c. 420 in^3
d. 750 in^3

Where B₁ and B₂ are the areas of the bases, the volume of the frustum is given by

... V = (1/3)(B₁ +B₂ +√(B₁B₂))h

For your dimensions, the volume is

... V = (1/3)(100 + 25 + √(100·25))·12 = (1/3)·175·12 = 700

The appropriate choice for the volume of the frustum is

... B. 700 in³

Since the triangle is a right triangle, you can use the Pythagorean Theorem to find the length of the hypotenuse.
The Pythagorean Theorem: a² + b² = c², where c is the hypotenuse of the triangle.

Plug in the leg lengths and solve.

    a² + b² = c²
    3² + 4² = c²
    9 + 16 = c²
          25 = c²
            5 = c

The length of the hypotenuse is 5 ft.