Question
If the cylinder and the cone shown have the same volume, then the radius and height of the cone could be which of these? (2 points) Responses radius of the cone = 15; height of the cone = 4 radius of the cone = 15; height of the cone = 4 radius of the cone = 15; height of the cone = 12 radius of the cone = 15; height of the cone = 12 radius of the cone = 5; height of the cone = 12 radius of the cone = 5; height of the cone = 12 radius of the cone = 5; height of the cone = 4
Answers
GPT 3.5
To find the volume of a cylinder or cone, we use the formula:
Volume of a cylinder = πr^2h
Volume of a cone = (1/3)πr^2h
Given that the volumes of the cylinder and cone are equal, we can set up the following equation:
π(8)^2(5) = (1/3)πr^2h
Simplify the equation:
64π(5) = (1/3)πr^2h
320π = (1/3)πr^2h
960 = r^2h
Now we can check the options to see which combination of radius and height satisfies this equation.
Option 1: radius = 15, height = 4
(15)^2(4) = 900
Option 2: radius = 15, height = 12
(15)^2(12) = 2700
Option 3: radius = 5, height = 12
(5)^2(12) = 300
Option 4: radius = 5, height = 4
(5)^2(4) = 100
Therefore, the combination that satisfies the equation is:
radius of the cone = 5; height of the cone = 12
Volume of a cylinder = πr^2h
Volume of a cone = (1/3)πr^2h
Given that the volumes of the cylinder and cone are equal, we can set up the following equation:
π(8)^2(5) = (1/3)πr^2h
Simplify the equation:
64π(5) = (1/3)πr^2h
320π = (1/3)πr^2h
960 = r^2h
Now we can check the options to see which combination of radius and height satisfies this equation.
Option 1: radius = 15, height = 4
(15)^2(4) = 900
Option 2: radius = 15, height = 12
(15)^2(12) = 2700
Option 3: radius = 5, height = 12
(5)^2(12) = 300
Option 4: radius = 5, height = 4
(5)^2(4) = 100
Therefore, the combination that satisfies the equation is:
radius of the cone = 5; height of the cone = 12