Question

The volumes of two cubes are 32ft^3 and 1372ft^3

1. What is the ratio of their volumes?
2. What is the scale factor?
3. What is the ratio of their surface areas?
4. Find the surface are of the smaller cube if the larger cube has a surface area of 196ft^2

Answer 1

1) 8 : 343

2) 42.875 or 42 ⅞

3) 4 : 49

4) 16ft²

Explanation:

Volume of cube: s³

Surface area of cube: 6s²

_____________________

32ft^3 and 1372ft^3 →

32 : 1372 = 8 : 343

343 / 8 = 42 ⅞ = 42.875

s³ → 6s²

s³ = 8, s = 2, s² = 4.

s³ = 343, s = 7, s² = 49.

These are proportional so it is already in the simplest ratio so it is not necessary to multiply by 6.

s³ → 8 : 343

6s² → 4 : 49

(4 / 49) × 196ft² = 16ft²