Question

Cone a and cone b both have a height of 5 in. The volume of cone a is 20.9cubic in, the volume of cone b is 4 times the volume of cone a, about how many times longwr is the diameter of cone b than the diameter of cone a?

Answer 1

Answer: two times

Explanation:

Given

height of cone A and B
`h_a=h_b=5\ in.`

The volume of cone A
`V_a=20.9\ in.^3`

The volume of cone B is 4 times of cone A

the volume of a cone is
`(1)/(3)\pi r^2h`

The volume of cone A

`V_a=(1)/(3)\pi r_a^2h_a=20.9\quad \ldots(i)`

The volume of cone B

`V_b=(1)/(3)\pi r_b^2h_b=4* 20.9\quad \ldots(ii)`

divide (i) and (ii) we get

`\Rightarrow (r_a^2)/(r_b^2)=(1)/(4)\\\Rightarrow (r_a)/(r_b)=\sqrt{(1)/(4)}=(1)/(2)\\\Rightarrow (d_a)/(d_b)=(1)/(2)\\\Rightarrow d_b=2d_a`

thus, diameter of cone B is twice the diameter of A