a cylinder with a diameter of 24 inches and a height of 8 inches has the same volume as a cone with a diameter of 12 inches. what is the height of the cone?

Accepted Solution

Answer:The height of the cone is 97 inStep-by-step explanation:Equate the formulas for the volume of a cylinder and that of a cone:Vol-Cyl              Vol-Coneπr²h         =        (1/3)πr²hNow cancel out items that are the same on both sides (π):r²h             =         (1/3)r²hNow substitute the given values for both solids:(12 in)²(8 in)  =  (1/3)(6 in)²(h-cone)                                  1152 in³Then (h-cone) = --------------------  =  97 in                                    12 in²The height of the cone is 97 in