The ratio of the corresponding linear measures of two similar cans of vegetables is 4 to 5. The smaller can has a surface area of 400 square centimeters. Find the surface area of the larger can.

Answer 1

linear measures of 2 cans is 4:5

surface area of smaller can is 400 cm^2

surface area of the larger can is 625 cm^2

let the smaller can be 4x4x4

the larger 5x5x5

surface area of smaller = 6x16 = 96 cm^2

surface area of larger = 6x25 = 150 cm^2

150/96 = 25/16 = 5^2/4^2

if the smaller is 400 cm^2

the ratio of larger to smaller surface area = L^2/s^2

= L^2/400 = L^2/20^2 =25^2/20^2 since 25:20 = 5:4

L^2 = 25^2= 625 cm^2