First, we need to calculate the volume of the cylinder and the cone separately, and then add them together to get the total volume of the tin man's head.
The formula for the volume of a cylinder is Vcylinder = πr^2h, where r is the radius and h is the height. Plugging in the values, we get:
Vcylinder = π(4^2)(12) = π(16)(12) = 192π
Next, the formula for the volume of a cone is Vcone = (1/3)πr^2h. Plugging in the values, we get:
Vcone = (1/3)π(4^2)(6) = (1/3)π(16)(6) = 32π
Finally, adding the volumes of the cylinder and the cone, we get the total volume of the tin man's head:
Vtotal = Vcylinder + Vcone = 192π + 32π = 224π
Therefore, the volume of the tin man's head in terms of π is 224π cubic inches.
A Tin man has a head that is a cylinder with a cone on top. The height of the cylinder is 12 inches and the height of the cone is 6 inches. The radius of both the cylinder and the cone is 4 inches. What is the volume of the tin man's head in terms of pi?
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