Question

if the slant height of a cone is double its base radius then the volume of the cone is​

Answer 1

Answer:

Hence, Volume of cone is πr 3 3 u n i t 3

Step-by-step explanation:

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Answer 2

Answer: The volume of the cone is proportional to the cube of the base radius, and in this case, it is (√3/3)πr^3.

Step-by-step explanation:

The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the base radius and h is the height. Let the base radius of the cone be denoted by r, and the slant height be denoted by l.

Given, l = 2r.

Using the Pythagorean theorem, we have l^2 = r^2 + h^2.

Substituting the given value of l, we get:

(2r)^2 = r^2 + h^2

4r^2 = r^2 + h^2

3r^2 = h^2

We can substitute this value of h^2 in the formula for volume:

V = (1/3)πr^2h

V = (1/3)πr^2(√(3r^2))

V = (√3/3)πr^3

Thus, the volume of the cone is proportional to the cube of the base radius, and in this case, it is (√3/3)πr^3.

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