A box in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12 cubes

measuring 6 inches on each side

If the length and width of the base are doubled, how many cubes could the new box hold?

18

24

48

96

number of cube the new box can hold = 10368 / 216 = 48

Step-by-step explanation:

The rectangular prism has the dimension of 12 by 18 by 12 inches. The volume of the rectangular prism can be expressed as

volume of rectangular prism = LWH

where

L = length

W = width

H = height

volume of rectangular prism = LWH

Volume of rectangular prism = LWH

Volume of rectangular prism = 12 * 18 * 12 = 2592 inches³

Volume of cube = L³

Volume of cube = 6³ = 216 inches³

The actual number of cube wood according to the question the prism can hold will be = 2592/216 = 12 cubes

When the length and width of the base are doubled. The volume will be as follows

volume of the prism = LWH

L = 12 * 2 = 24 inches

W = 18 * 2 = 36 inches

volume of the prism = 24 * 36 * 12 = 10368 inches³

number of cube the new box can hold = 10368 / 216 = 48