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.

`\frac{\text{Area of box A}}{\text{Area of box B}}=\frac{(\text{Side of box A})^2}{(\text{Side of box B})^2}`

`(98)/(A_B)=((a)^2)/((4a)^2)`

`(98)/(A_B)=((a)^2)/(16a^2)`

`(98)/(A_B)=(1)/(16)`

Using cross multiplication, we get

`98* 16=1* A_B`

`1568=A_B`

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