Question

The volumes of two similar solids are 1331 m3 and 216 m3. the surface area of the larger solid is 324 m3. what is the surface area of the smaller solid?

Answer 1

surface area of the smaller solid will be 96.40m².

Explanation:

Volumes of two similar solids are 1331 m³ and 216 m³

Since volume is a three dimensional unit means its a multiplication of 3 dimensions, so cube root of ratio of volume gives us the ratio of dimensions.

`(V_(1) )/(V_(2))=(216)/(1331)=\sqrt[3]{(216)/(1331)}=(6)/(11)`

Similarly ratio of surface areas will be equal to the square of the ratio of dimensions.

`(S_(1) )/(S_(2))=((6)/(11))^(2)`

`(S_(1) )/(324)=((36)/(121))`

By cross multiplication

`S_(1)(121)=36(324)`

`S_(1)=(36*324)/(121)=96.40m^(2)`

therefore, surface area of the smaller solid will be 96.40m².

Answer 2

Two solids are said to be similar when their corresponding sides and angles are proportional and congruent. Since the solids here are similar, we calculate as follows:

Assuming the solid is a sphere
V1/V2 = r1^3 / r2^3 = 1331/216 = 6.16203
r1/r2 = 11/6

A1/A2 = (r1/r2)^2
324/A2 = (11/6)^2
A2 = 42.84 m^2