Answer:
The approximate height is 8.9 cm
Step-by-step 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[tex]\frac{h}{3}[/tex]
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= [tex]\frac{d}{2}[/tex] 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[tex]\frac{h}{3}[/tex]
225 ≈ 3.14 × 5² × [tex]\frac{h}{3}[/tex]
225 ≈ 78.5 ×[tex]\frac{h}{3}[/tex]
225 ≈ [tex]\frac{75.8 h}{3}[/tex]
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
