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.
[tex]\dfrac{\text{Area of box A}}{\text{Area of box B}}=\dfrac{(\text{Side of box A})^2}{(\text{Side of box B})^2}[/tex]
[tex]\dfrac{98}{A_B}=\dfrac{(a)^2}{(4a)^2}[/tex]
[tex]\dfrac{98}{A_B}=\dfrac{(a)^2}{16a^2}[/tex]
[tex]\dfrac{98}{A_B}=\dfrac{1}{16}[/tex]
Using cross multiplication, we get
[tex]98\times 16=1\times A_B[/tex]
[tex]1568=A_B[/tex]
Therefore, the surface area of box B is 1568 in².
