Question

A formula for the surface area $\left(A\right)$ of the rectangular solid shown below is $A=2lw+2lh+2wh$ where $l$ represents length; $w$, width; and $h$, height. By doubling each of the dimensions ($l,w$, and $h$), the surface area will be multiplied by what factor?

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

Answer: (B)

$4$

Original area $A=2lw+2lh+2wh$

Now if each dimensions are doubled, then

New are will be $A^{\prime }=2\left(2l\right)\left(2w\right)+2\left(2l\right)\left(2h\right)+2\left(2w\right)\left(2h\right)=4(2lw+2lh+2wh)=4A$

So if all dimensions are doubled then surfaced area will multiplied by factor of $4$