Question

Find the missing dimension of the cone round to the nearest tenth volume=3.6 in and height 4.2 in .What is the diameter

Answer 1

we know the equation for the volume of a cone is pi*r^2 h/3=3.6
pi r^2 *4.2=10.8
solve for r
r is about 0.9 so diameter is 1.8 in

Answer 2

The diameter of the cone is 1.8 inches.

Explanation:

Let r be the radius of the cone,

Since, we know that,

The volume of a cone is,

`V=(1)/(3)\pi R^2 h`

Where, R is the radius of the cone,

h is the height of the cone,

We have, V = 3.6 in², h = 4.2 in

`3.6 = (1)/(3)\pi (r)^2(4.2)`

`10.8 = \pi(r)^2(4.2)`

`(10.8)/(4.2)=\pi (r)^2`

`\implies r = \sqrt{(10.8)/(4.2\pi)}=0.905\text{ in}`

Hence, the diameter of the cone = 2r = 2 × 0.905 = 1.81 ≈ 1.8 inches.