Question

18 The three solids A, B and C are similar such that

and
the surface area of A: the surface area of B=4:9
the volume of B: the volume of C = 125:343
Work out the ratio
the height of A: the height of C
Give your ratio in its simplest form.

Answer 1

1:1

Explanation:

Since the surface area of A is 4 times the surface area of B, and the volume of B is 125 times the volume of C, we can write the following proportion:

(surface area of A) / (surface area of B) = (volume of B) / (volume of C)

(height of A)^2 / (height of B)^2 = (height of B)^3 / (height of C)^3

We can then cross-multiply and simplify to find the ratio of the heights:

(height of A)^2 / (height of C)^2 = (height of B)^3 / (height of B)^3

(height of A)^2 = (height of C)^2

Therefore, the ratio of the height of A to the height of C is 1:1, or simply 1.