An architect

An architect is designing a house. He wants the bedroom to have the dimensions of 8 ft by 4 ft by 7 ft. The architect doubles all three dimensions to create the den. Does that mean the den will have double the volume of the bedroom?
First, find the volume of the bedroom.
Solve on paper.

Does doubling all three dimensions mean the den will have to double the volume of the bedroom? Why or why not?

Correct answer:

V₁ =  224 ft³
V₂ =  1792 ft³

Step-by-step explanation:

$$\begin{gathered} a=8\text{ft} \\ b=4\text{ft} \\ c=7\text{ft} \\ {V}_1=a\cdot b\cdot c=8\cdot 4\cdot 7=224{\text{ft}}^3 \end{gathered}$$

$$\begin{gathered} x=2\cdot a=2\cdot 8=16\text{ft} \\ y=2\cdot b=2\cdot 4=8\text{ft} \\ z=2\cdot c=2\cdot 7=14\text{ft} \\ {V}_2=x\cdot y\cdot z=16\cdot 8\cdot 14=1792=1792{\text{ft}}^3 \\ k=V_2/V_1=1792/224=8 \end{gathered}$$

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