Multiple choice

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?

  1. $2$
  2. $4$
  3. $6$
  4. $8$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If dimensions l, w, h are doubled to 2l, 2w, 2h, the new surface area is 2(2l)(2w) + 2(2l)(2h) + 2(2w)(2h) = 8lw + 8lh + 8wh = 4(2lw + 2lh + 2wh). The area is multiplied by 4.

AI explanation

The formula for the surface area of a rectangular solid is A = 2lw + 2lh + 2wh. If each dimension is doubled, the new surface area becomes 2(2l)(2w) + 2(2l)(2h) + 2(2w)(2h), which simplifies to 8lw + 8lh + 8wh. This factors to 4(2lw + 2lh + 2wh), showing the new surface area is exactly 4 times the original surface area.

Keep practicing — related questions