Question

The volume of a right cone is 100π
units3. If its height is 12 units, find its diameter.

Answer 1

Answer: 10 units

Explanation:

We can use the following formula to determine the diameter of this cone. V is equal to volume, r is equal to radius (half of the diameter), and h is equal to height.

`\displaystyle \boxed{r=\sqrt{3(V)/(\pi h)} }`

Given:

`\displaystyle r=\sqrt{3(V)/(\pi h)}`

Substitute known values:

`\displaystyle r=\sqrt{3(100\pi)/(\pi (12))}`

Divide:

➜
`(\pi)/(\pi)=1`, so we are left with 100 divided by 12

`\displaystyle r=\sqrt{3((25)/(3) )}}`

Multiply:

➜ When multiplying, we can think of it as
`(3)/(1) *(25)/(3)`.
`(3)/(3) =1`, so we are left with 25.

`\displaystyle r=√(25)`

Square root:

r = 5, r = -5

Since it's a measure of a shape, it cannot be negative. This means the radius is equal to 5. Now, we will find the diameter.

5 units * 2 = 10 units