Question

If a CONE has a DIAMETER of 10 centimeters and a Volume of 225 cubic centimeters, what is its approximate HEIGHT

Answer 1

The approximate height is 8.9 cm

Explanation:

To find the height of a cone with a diameter of 10 cm and a volume of 225 cubic centimeter, we will follow the steps below;

first, write down the formula for finding the volume of a cone

v=πr²
`(h)/(3)`

where v is the volume of the cone

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

from the question given,

diameter = 10 cm but d=2r this implies that r=
`(d)/(2)` r= 10/2 = 5cm

hence r= 5cm

Also v= 225 cm³

π is a constant and is ≈ 3.14

We can now proceed to insert the values into formula and then solve for h

v=πr²
`(h)/(3)`

225 ≈ 3.14 × 5² ×
`(h)/(3)`

225 ≈ 78.5 ×
`(h)/(3)`

225 ≈
`(75.8 h)/(3)`

cross-multiply

675 = 75.8 h

divide both-side of the equation by 75.8

8.9 ≈ h

h≈ 8.9

Therefore, the approximate height is 8.9 cm