Question

A cardboard box is open at one end and is shaped like a square prism missing one of its square bases. The volume of the prism is 810 cubic inches, and its height is 10 inches. A. What is the length of each side of the base? B. How much cardboard is used for the box?

Answer 1

Given:
Volume of square prism = 810 cubic inches
Height of square prism = 10 inches

The volume of a square prism has this formula:
v = a²h

a = side length of the square prism
h = height

810 in³ = a² * 10in
810 in³ ÷ 10 in = a²
81 in² = a²
√81 in² = √a²
9 in = a

The length of each side of the base is 9 inches. Only 5 sides of the cardboard box has a cardboard because the 6th side is open.

Answer 2

Since the dimensions have a proportional relationship, the new volume can be calculated using the original volume and the scale factor. The new volume will be the cube of the change, which is 1 /64 . The new volume is the product of 6,336 and 1 /64 .