Question

The height of a filing cabinet is 1.5 times the width. The depth is twice the width.The volume of the cabinet is 12,288 in³. What are the cabinet's dimensions?

Answer 1

width = 16 in

height = 24 in

depth = 32 in

Step-by-step explanation:

Volume = height x width x depth = hwd

h = 1.5w

d = 2w

V = (1.5w)(w)(2w) = 12,288

V = 3w³ = 12,288

w³ = 12,288/3 = 4096

w = ∛4096 = 16

h = 1.5(16) = 24

d = 2(16) = 32

Answer 2

The dimensions of the filing cabinet are: Width: 16 inches, Height: 24 inches, Depth: 32 inches.

Step-by-step explanation:

Let's assume the width of the filing cabinet is x inches. According to the given information:

• The height of the filing cabinet is 1.5 times the width, so the height is 1.5x inches.
• The depth is twice the width, so the depth is 2x inches.

To calculate the volume of the cabinet, we multiply the length, width, and height:
Volume = length x width x height = x x 1.5x x 2x = 12,288 in³

Now we can solve the equation:

12,288 = 3x³

Dividing both sides by 3:

x³ = 4,096

Taking the cube root of both sides, we find that the width (x) is approximately 16 inches.

Therefore, the dimensions of the filing cabinet are:

• Width: 16 inches
• Height: 1.5 times the width = 1.5 x 16 = 24 inches
• Depth: twice the width = 2 x 16 = 32 inches