two cubes have volumes of 64 cubic feet and 216 cubic feet. what is the ratio of the surface area of the smaller cube to the surface area of the larger cube?

Question

apparently i have to add details so um usually when i do ratio i do it in a fraction small/big instead of the standard small:big just because im lazy and my teachers fine with it lmao but if u wanna give the answer as small:big that’s fine too lmao

Answer 1

Very easy, River! Cubes have the friendliest formula you ever did see:

V = S³

Since you were given the volumes, simply plug them into the equation one at a time. In each case, you find the S by cube rooting both sides, which gets you:

S = 4       ,         S = 6

Area, on the other hand, is a perfect square:

A = S²

Your areas are, respectively,

A = 16    ,          A = 36

Simply write them as a ratio and remember to reduce to lowest terms!

Answer 2

volumes are 4³ and 6³ respectively so the surface areas will have ratio 4² and 6² respectively, ie. 16:36 which reduces to 4:9

Answer 3

PROBLEM

 

two cubes have volumes of 64 cubic feet and 216 cubic feet. what is the ratio of the surface area of the smaller cube to the surface area of the larger cube?
apparently i have to add details so um usually when i do ratio i do it in a fraction small/big instead of the standard small:big just because im lazy and my teachers fine with it lmao but if u wanna give the answer as small:big that’s fine too lmao

 

SOLUTION

 

When comparing geometric figures, if a = smaller figure dimension and b = larger figure dimension, then for

 

Ratios:

 

1-dimension:     a : b

 

2-dimensions:   a² : b²

 

3-dimensions:   a³ : b³

 

In this problem, you're dealing with volume, so you look at the ratios for three dimensions, take the cube root of both volumes to find the length of each cube (a = small length, b = large length), then square those dimensions to find the ratio of the surface areas.

 

If you need help going through the process, please feel free to contact me...