Question

Box A has a surface area of 98 in 2. If box B is 4 times the size of box A, what is the surface area of box B?

Answer 1

Given:

Box A has a surface area of 98 in².

Box B is 4 times the size of box A.

To find:

The surface area of box B.

Solution:

Let "a" be the side of box A , then "4a" be the side of box B because box B is 4 times the size of box A.

We know that the areas of similar figures are proportional to the square of their corresponding sides.

$\dfrac{\text{Area of box A}}{\text{Area of box B}}=\dfrac{(\text{Side of box A})^2}{(\text{Side of box B})^2}$

$\dfrac{98}{A_B}=\dfrac{(a)^2}{(4a)^2}$

$\dfrac{98}{A_B}=\dfrac{(a)^2}{16a^2}$

$\dfrac{98}{A_B}=\dfrac{1}{16}$

Using cross multiplication, we get

$98\times 16=1\times A_B$

$1568=A_B$

Therefore, the surface area of box B is 1568 in².