Ahmed received a box of gifts. The box is a rectangular prism with the same height and width, and the length

is twice the width. The volume of the box is 3,456 in? What is the height of the box?

Answer:

12 inches

Step-by-step explanation:

Ahmed received a box of gifts. The box is a rectangular prism with the same height and width, and the length

is twice the width. The volume of the box is 3,456 in? What is the height of the box?

Volume of a Rectangular pyramid = Length × Width × Height

From the above question

Height = Width = x

Length = 2 × Width

Length = 2x

Volume = 3,456 cubic inches

Hence,

3,456 = 2x × x × x

3456 = 2x³

x³ = 3456/2

x³ = 1728

Cube root both sides

Cube root(x³) = cube root (1728 cubic Inches)

x = 12 inches

Therefore, the height is 12 inches

Width, Height and Length of rectangular prism are 12, 12 and 24 inch respectively.

Width of rectangular prism = a

Height of rectangular prism = a

Length of rectangular prism = 2a

Volume of the rectangular prism = (l)(b)(h)

Volume of the rectangular prism = (2a)(a)(a)

3,456 = 2a³

a³ = 1,728

a = 12 inch

So,

Width of rectangular prism = 12 inch

Height of rectangular prism = 12 inch

Length of rectangular prism = 2(12)

Length of rectangular prism = 24 inch

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