The volume of this cone is 83.7 cubic meters. Find the DIAMETER. SHOW ALL WORK

Question

asked Apr 22, 2022 45.5k views

2 Answers

Percutio · Answer 1 · 2022-04-24T17:27:53+0000

Given: Volume of the cone is 83.7 m³

We know that:

$\bigstar \ \ \boxed{\sf{\textsf{Volume of cone is given by} : (\pi r^2h)/(3)}}$

where r is the radius of the cone and h is the height of the cone

Given: Height of the cone = 5m

Substituting the values in the formula, we get:

$\sf{\implies (\pi r^2(5))/(3) = 83.7}$

$\sf{\implies \pi r^2 = 83.7 * (3)/(5)}$

$\sf{\implies \pi r^2 = 83.7 * 0.6}$

$\sf{\implies \pi r^2 = 50.22}$

$\sf{\implies r^2 = (50.22)/(\pi)}$

$\sf{\implies r^2 = 16}$

$\sf{\implies r = 4}$

We know that : Diameter is two times the radius

⇒ Diameter of the Cone is 8 meters