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
288π cm3
288π cm3
216π cm3
216π cm3
360π cm3
360π cm3
144π cm3
144π cm3
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To find the volume of the frozen yogurt in the cone and hemisphere, we need to find the volumes of the cone and the hemisphere separately and then add them together.
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height. Substituting the given values, the volume of the cone is V = (1/3)π(6^2)(24) = 288π cm^3.
The volume of a hemisphere is given by the formula V = (2/3)πr^3. Substituting the given radius, the volume of the hemisphere is V = (2/3)π(6^3) = 288π cm^3.
Adding the volumes of the cone and hemisphere, we get 288π + 288π = 576π cm^3.
Therefore, the exact volume of the frozen yogurt in the cone and hemisphere is 576π cm^3.