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1. The lateral area of two similar cylinders is 64 m2 and 144 m2. The volume of the larger cylinder is 216 m3. What is the volume of the smaller cylinder?
CAN SOMEONE PLEASE HELP WITH THIS QUESTION!!!

Respuesta :

Answer:

64 m³

Step-by-step explanation:

For similar figures

linear ratio = a : b , then

area ratio = a² : b² and

volume ratio = a³ : b³

Given

area ratio = 64 : 144 , then

linear ratio = [tex]\sqrt{64}[/tex] : [tex]\sqrt{144}[/tex] = 8 : 12 = 2 : 3

Then

volume ratio = 2³ : 3³ = 8 : 27

let volume of smaller cylinder be x, then

[tex]\frac{8}{x}[/tex] = [tex]\frac{27}{216}[/tex] ( cross- multiply )

27x =  8 × 216 = 1728 ( divide both sides by 27 )

x = 64

Volume of the smaller cylinder = 64 m³

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