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
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