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)
[tex] (\frac{A}{B})^2= (\frac{9}{16}) [/tex]
Take the square root of both sides:
[tex] (\sqrt{\frac{A}{B}})^2 = (\sqrt{\frac{9}{16}}) [/tex]
[tex] \frac{A}{B} = \frac{3}{4}[/tex]
Ratio of volume of shape B to C = 27:125
Thus,
(B:C)³ = 27:125
[tex] (\frac{B}{C})^3= (\frac{27}{125}) [/tex]
Take the cube root of both sides:
[tex](3\sqrt{\frac{B}{C}})^3 = (3\sqrt{\frac{27}{125}})[/tex]
[tex] \frac{B}{C} = \frac{3}{5}[/tex]
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
