Question

A cone has a radius of 20cm and a volume of 925cm to the 3rd power. what is the volume of a similar cone with a radius of 10 cm?

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Answer 1

115.625 cm³

Explanation:

For 2 similar shapes

linear ratio = a : b, then

volume ratio = a³ : b³

The ratio of the radii = 20 : 10 = 2 : 1, thus

The ratio of the volumes = 2³ : 1³ = 8 : 1

Let x be the volume of the smaller cone, then

`(x)/(1)` =
`(925)/(8)` ( cross- multiply )

8x = 925 ( divide both sides by 8 )

x = 115.625

The volume of the smaller cone = 115.625 cm³

Answer 2

115.625 cm³

Explanation:

The ratio of the volumes is in proportion with the cube of the proportion of the lengths.

V1/925 = (10/20)³

V1/925 = (1/2)³

V1/925 = 1/8

V1 = 925 ÷ 8

V1 = 115.625 cm³