Question

Three solid shapes A,B and C The surface area of shape A is 9cm² The surface area of shape B is 16cm² The ratio of the volume of shape B to the volume of shape C is 27 : 125 Work out the ratio of the height of shape A to the height of shape C

Answer 1

Answer:

9:20

Step-by-step explanation:

Given:

Surface area of shape A = 9 cm²

Surface Area of shape B = 16 cm²

Ratio of volume of shape A to B = 27:125

Required:

Find the ratio of the height of shape A to the height of shape C.

Ratio of surface area (A:B)² = ratio of linear measures (A:B)

Thus,

(A:B)² = (A:B)

(A/B)² = (A/B)

$(\frac{A}{B})^2= (\frac{9}{16})$

Take the square root of both sides:

$(\sqrt{\frac{A}{B}})^2 = (\sqrt{\frac{9}{16}})$

$\frac{A}{B} = \frac{3}{4}$

Ratio of volume of shape B to C = 27:125

Thus,

(B:C)³ = 27:125

$(\frac{B}{C})^3= (\frac{27}{125})$

Take the cube root of both sides:

$(3\sqrt{\frac{B}{C}})^3 = (3\sqrt{\frac{27}{125}})$

$\frac{B}{C} = \frac{3}{5}$

Therefore, ratio of lengths A:B:C =

3:4:C

A:3:5

To make them equivalent, we have:

9:12:C

A:4:20

Therefore, the ratio of the height of shape A to the height of shape C =

9:20