Question

The formula for the volume of a cone is V= 1/3pir^2h where V represents the volume, r represents the radius of the base, h represents the height. What is the height of a cone with a volume of 66 cubic centimeters and a base with a radius of 3 centimeters?

Answer 1

The height of the cone is approximately 7.01 centimeters.

We know the volume (V) is 66 cubic centimeters and the radius (r) is 3 centimeters. Substitute these values into the formula:

V = 1/3πr²h

66 = 1/3 × π × 3² × h

Simplify the equation:

Multiply both sides by 3:

200 = π × 9 × h

Cancel out the common factor of 9:

200/9 = π × h

Solve for the height (h):

Divide both sides by π:

h = 200/9π

Then, we have that;

h ≈ 7.01 cm

Therefore, the height of the cone is approximately 7.01 centimeters.

Answer 2

H = 7cm

Explanation:

Volume of a cone = V = ⅓πr²h

H = ?

R = 3cm

V = 66cm³

π = 3.14

V = ⅓ * π * r² * h

66 = ⅓ × 3.14 × 3² × h

66 = ⅓ * 28.26h

3 * 66 = 28.26h

198 = 28.26h

H = 198 / 28.26

H = 7cm

The height of the cone is 7cm