Question

A shoe box has a volume of 64 cubic inches and a surface area of 160 square inches. What is the surface area of a similar shoe box if its volume is only 27 cubic inches? Show your work or explain how you got your answer.

Answer 1

we can figure it out by ratio

volume/ surface area = volume / surface area

64/160 = 27 / x

64x = 4320

x = 67.5 cm²

Answer 2

Answer:

SA = 90 in²

Step-by-step explanation:

given 2 similar shapes with sides in ratio a : b , then

ratio of areas = a² : b²

ratio of volumes = a³ : b³

Given ratio of volumes = 64 : 27 , then

ratio of sides = $\sqrt[3]{64}$ : $\sqrt[3]{27}$ = 4 : 3

then ratio of areas = 4² : 3² = 16 : 9

let x be the surface area of the smaller box then by proportion

$\frac{x}{9}$ = $\frac{160}{16}$ = 10 ( multiply both sides by 9 )

x = 90

surface area of smaller box is 90 in²