Question

Consider the right circular cone below:
a) 4 m
b) 6 m

Answer 1

a) 4 m

b) 6 m

The volume ratio as 4:6, taking the cube root yields the linear ratio as
`(4/6)^(1/3) ≈ 0.873`. Therefore, the linear ratio of the dimensions (radius and height) of the cones is approximately 0.873:1.

Step-by-step explanation:

The volume of a right circular cone is given by the formula V =
`(1/3)πr^2h,`where 'r' is the radius of the base and 'h' is the height. For two right circular cones with equal volumes but different dimensions, considering the volume ratio V₁/V₂ =
`(r₁^2h₁)/(r₂^2h₂)`, if the volumes are in the ratio 1:1, then the dimensions must be in the ratio (r₁/r₂)² = (h₁/h₂). When given the ratio of volumes, to find the ratio of dimensions, the cube root of the volume ratio must be taken, giving the linear ratio of dimensions.

Given the volume ratio as 4:6, taking the cube root yields the linear ratio as
`(4/6)^(1/3) ≈ 0.873`. Therefore, the linear ratio of the dimensions (radius and height) of the cones is approximately 0.873:1. Applying this ratio to the given dimensions a) 4m and b) 6m, the corresponding dimensions would be approximately 3.492m and 5.238m, rounded to one decimal place.