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.