Question

the formula for the volume of a cylinder is V=3.14r^2h. The volume of a cylinder is 3 times the volume of a cone with the same radius and height. If the volume of a cone with the same height as a cylinder equals the volume of the cylinder, the equation for the radius of cone R in terms of the radius of a cylinder is?

Answer 1

The equation for the radius of cone R in terms of the radius of cylinder (r) is,

R = r√3

Explanation:

Volume of the cone = πR²H/3 (where Height is H and Radius is R)

Volume of the Cylinder = πr²h (where Height is h and Radius is r)

Now, both are same in height, so H = h and Their volume are same. So,

πR²H/3=πr²h

or, R²/3=r²

or, R²=r²×3

or, R = √(r²×3)

or, R = r√3

Answered by GAUTHMATH