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

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743