The ratio of the corresponding linear measures of two similar cans of vegetables is 5 to 8. The smaller can has a surface area of 300 square centimeters. Find the surface area of the larger can.

Answer 1

We cannot scale 5:8 with 300:x directly. Linear measures and Area measures are not proportional.

To illustrate this, consider square with side length 2 and area 4 (2^2 = 4).

If we make the side length 3, the area becomes 9.

We scaled the length by 3/2, and the area scaled by 9/4, which is (3/2)^2.

Area scales by the sqaure of the scale of lengths.

Our linear scale is 8/5. Square this ratio, and set it equal to x/300. Cross multiply and solve.

64/25 = x/300. Solve for x