Question
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?
Responses
A 192π 192π in ^3
B 224π 224π in ^3
C 384π 384π in ^3
D 912π in ^3
Responses
A 192π 192π in ^3
B 224π 224π in ^3
C 384π 384π in ^3
D 912π in ^3
Answers
GPT 3.5
C 384π in ^3
To find the volume of the cylinder with radius 4 inches and height 12 inches, we use the formula V_cylinder = πr^2h = π(4)^2(12) = 192π cubic inches.
To find the volume of the cone with radius 4 inches and height 6 inches, we use the formula V_cone = 1/3πr^2h = 1/3π(4)^2(6) = 32π cubic inches.
Adding the volumes of the cylinder and cone together, we get a total volume of 192π + 32π = 224π cubic inches.
To find the volume of the cylinder with radius 4 inches and height 12 inches, we use the formula V_cylinder = πr^2h = π(4)^2(12) = 192π cubic inches.
To find the volume of the cone with radius 4 inches and height 6 inches, we use the formula V_cone = 1/3πr^2h = 1/3π(4)^2(6) = 32π cubic inches.
Adding the volumes of the cylinder and cone together, we get a total volume of 192π + 32π = 224π cubic inches.