An architect 2

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.

Result

x=

Yes

No

Step-by-step explanation:

$$\begin{gathered} a=8\text{ft} \\ b=4\text{ft} \\ c=7\text{ft} \\ {V}_1=a\cdot b\cdot c=8\cdot 4\cdot 7=224{\text{ft}}^3 \\ {a}_2=2\cdot a=2\cdot 8=16\text{ft} \\ {b}_2=2\cdot b=2\cdot 4=8\text{ft} \\ {c}_2=2\cdot c=2\cdot 7=14\text{ft} \\ {V}_2=a_2\cdot b_2\cdot c_2=16\cdot 8\cdot 14=1792{\text{ft}}^3 \\ n=V_2/V_1=1792/224=8 \\ x=0 \end{gathered}$$

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