To determine which combination of radius and height for the cone will result in the same volume as the cylinder, we need to use the formula for the volume of a cylinder and a cone.
The volume of a cylinder is given by V_cylinder = πr^2h, where r is the radius of the cylinder and h is the height of the cylinder.
The volume of a cone is given by V_cone = (1/3)πr^2h, where r is the radius of the cone and h is the height of the cone.
Since the volume of the cylinder and the cone are equal, we can set up the following equation:
πr_cylinder^2h_cylinder = (1/3)πr_cone^2h_cone
Canceling out the common factor of π and rearranging the equation, we get:
3r_cylinder^2h_cylinder = r_cone^2h_cone
Given that the radius of the cylinder is equal to 5 units (r_cylinder = 5 in this case) and the height of the cylinder is 12 units (h_cylinder = 12), we can substitute these values into the equation to solve for the radius and height of the cone.
3(5)^2(12) = r_cone^2h_cone
3(25)(12) = r_cone^2h_cone
900 = r_cone^2h_cone
Now we need to look at the given options for the radius and height of the cone:
1. radius of the cone = 5; height of the cone = 12
2. radius of the cone = 15; height of the cone = 12
3. radius of the cone = 5; height of the cone = 4
4. radius of the cone = 15; height of the cone = 4
Substitute the values of radius and height in each option into the equation to determine if it results in 900:
For option 1: (5)^2(12) = 300 (not equal to 900)
For option 2: (15)^2(12) = 2700 (not equal to 900)
For option 3: (5)^2(4) = 100 (not equal to 900)
For option 4: (15)^2(4) = 900 (equal to 900)
Therefore, the correct combination of radius and height for the cone is: radius of the cone = 15; height of the cone = 4
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 = 5; height of the cone = 12 radius of the cone = 5; height of the cone = 12 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 = 4 radius of the cone = 5; height of the cone = 4 radius of the cone = 15; height of the cone = 4 radius of the cone = 15; height of the cone = 4 Skip to navigation
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