Question
The frozen yogurt cone shown is made from a cone and a hemisphere. The radius is 6 cm. The total height of the cone is 24 cm. The cone is completely packed with frozen yogurt.
What is the exact volume of the frozen yogurt in the cone and hemisphere? Leave your answer in terms of pi.
(1 point)
Responses
216π cm3
216π cm3
288π cm3
288π cm3
360π cm3
360π cm3
144π cm3
To find the volume of the frozen yogurt in the cone and hemisphere, we need to calculate the volumes of both shapes separately and then add them together.
First, let's find the volume of the cone. The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height.
Using the given information, we have r = 6 cm and h = 24 cm.
V(cone) = (1/3) π(6 cm)^2 * 24 cm = 288π cm^3
Next, let's find the volume of the hemisphere. The volume of a hemisphere is given by the formula V = (2/3)πr^3.
Again, using r = 6 cm as the radius of the hemisphere, we have:
V(hemisphere) = (2/3)π(6 cm)^3 = 288π cm^3
Finally, we can add the volumes of the cone and the hemisphere:
V(frozen yogurt) = V(cone) + V(hemisphere) = 288π cm^3 + 288π cm^3 = 576π cm^3.
Therefore, the exact volume of the frozen yogurt in the cone and hemisphere is 576π cm^3.