Question

an architect is designing a house . she wants the bedroom to have the dimensions 9ft by 4ft by 7ft. she doubles the dimensions to create the den. does that mean the den will have double the volume if the bedroom

Answer 1

Given:

a.) She wants the bedroom to have the dimensions 9ft by 4ft by 7ft.

b.) She doubles the dimensions to create the den.

From the given dimension, the bedroom appears to be in a rectangular prism. Applying the formula in getting the volume of a rectangular prism: Volume = L x W x H, let's determine what will happen to the volume after doubling its dimensions.

`\text{ Volume = L x W x H}`

Where,

L = Length = 9 Ft.

W = Width = 4 Ft.

H = Height = 7 Ft.

New dimension after being doubled:

L2 = 9 x 2 = 18 Ft.

W2 = 4 x 2 = 8 Ft.

H2 = 7 x 2 = 14 Ft.

Step 1: Let's determine the volume in its original dimensions.

`\text{ Volume = L x W x H}`
`\text{ = 9 x 4 x 7}`
`\text{ Volume = 252 Ft}^3`

Step 2: Let's determine the volume when the dimensions are doubled.

`\text{ Volume = L x W x H}`
`\text{ = 18 x 8 x 14}`

`\text{ Volume = 2016 Ft}^3`

Step 3: Let's determine the ratio of the two volumes.

`\text{ Ratio = }\frac{\text{ Volume when the dimensions are doubled}}{\text{ Volume at original dimensions}}`
`\text{ = }\frac{\text{ 2016}}{252}`
`\text{ Ratio = }8`

Therefore, the volume of the bedroom becomes 8 times larger when its dimensions are doubled.