Question

26. The volumes of two similar solids are 1,728 m3 and 343 m3. The surface area of the larger solid is 576 m2. What is the surface area of the smaller solid? (1 point)
196 m2
76 m2
1,372 m2
392 m2

Answer 1

well the ratio of volumes 343 :1728

well looking at the ratio of volumes its

\[\frac{1728}{343}\]

this ratio is the cube of the linear ratios...

so take the cube root of both to find the linear ratio...or linear scaling factor

\[\frac{\sqrt[3]{1728}}{\sqrt[3]{343}} = \frac{12}{7}\]

so the linear ratios are 12:7

now for area... the linear ratios are squared...

so the area ratios are

144 : 49

so then using the know infomation and letting x be the area of the smaller

\[\frac{576}{144} = \frac{x}{49}\]

solve for x to find the surface area of the smaller solid