Please help..not wanting answer just where to start... A cylinder has a radius of 5 centimeters and a height of 12 centimeters. What would the height of a cone need to be if it is the same volume and radius?

volume of cylinder = π(5^2)(12) = ...

volume of cone = (1/3)πr^2 h

solve (1/3)π(5^2)h = π(5^2)(12)

after getting your answer it should be obvious why it is so.

180

To find the height of a cone with the same volume and radius as a given cylinder, you can use the principle that the volume of a cylinder is equal to one-third the volume of a cone with the same base and height.

Here's how you can approach it step by step:

Step 1: Determine the volume of the cylinder. The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.

Given:
Radius of the cylinder (r) = 5 cm
Height of the cylinder (h) = 12 cm

Substituting the given values into the formula:
V_cylinder = π(5^2)(12) = 300π cubic centimeters

Step 2: Calculate the volume of the cone using the formula V_cone = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.

Given:
Radius of the cone (r) = 5 cm
Height of the cone (h) = ? (to be determined)

Substituting the given values into the formula:
300π = (1/3)π(5^2)h

Step 3: Solve for h, the height of the cone.

Multiply both sides of the equation by 3 to get rid of the fraction:
900π = π(5^2)h

Divide both sides of the equation by π(5^2) to isolate h:
h = (900π) / (π(5^2))

Simplifying the expression:
h = (900π) / (25π) = 36

Therefore, the height of the cone would need to be 36 centimeters to have the same volume and radius as the given cylinder.