Question

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

Answer 1

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$\frac{h}{3}$

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= $\frac{d}{2}$     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$\frac{h}{3}$

225 ≈ 3.14 × 5² × $\frac{h}{3}$

225 ≈ 78.5 ×$\frac{h}{3}$

225 ≈ $\frac{75.8 h}{3}$

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