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.%0D%0A%0D%0A%0D%0A%0D%0AWhat is the exact volume of the frozen yogurt in the cone and hemisphere? Leave your answer in terms of pi.%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A144π cm3%0D%0A144%0D%0A%0D%0A %0D%0A%0D%0A%0D%0A3%0D%0A144π cm3%0D%0A144%0D%0A%0D%0A %0D%0A%0D%0A%0D%0A3%0D%0A%0D%0A216π cm3%0D%0A216%0D%0A%0D%0A %0D%0A%0D%0A%0D%0A3%0D%0A216π cm3%0D%0A216%0D%0A%0D%0A %0D%0A%0D%0A%0D%0A3%0D%0A%0D%0A360π cm3%0D%0A360%0D%0A%0D%0A %0D%0A%0D%0A%0D%0A3%0D%0A360π cm3%0D%0A360%0D%0A%0D%0A %0D%0A%0D%0A%0D%0A3%0D%0A%0D%0A288π cm3

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.%0D%0A%0D%0A%0D%0A%0D%0AWhat is the exact volume of the frozen yogurt in the cone and hemisphere?  Leave your answer in terms of pi.%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A144π cm3%0D%0A144%0D%0A%0D%0A %0D%0A%0D%0A%0D%0A3%0D%0A144π cm3%0D%0A144%0D%0A%0D%0A %0D%0A%0D%0A%0D%0A3%0D%0A%0D%0A216π cm3%0D%0A216%0D%0A%0D%0A %0D%0A%0D%0A%0D%0A3%0D%0A216π cm3%0D%0A216%0D%0A%0D%0A %0D%0A%0D%0A%0D%0A3%0D%0A%0D%0A360π cm3%0D%0A360%0D%0A%0D%0A %0D%0A%0D%0A%0D%0A3%0D%0A360π cm3%0D%0A360%0D%0A%0D%0A %0D%0A%0D%0A%0D%0A3%0D%0A%0D%0A288π cm3

Bot GPT 3.5 · Answer

The volume of the cone can be calculated using the formula V = (1/3)πr^2h, where r is the radius and h is the height. Substituting the values given, we have V_cone = (1/3)π(6^2)(24) = 288π cm^3. The volume of the hemisphere can be calculated using the formula V = (2/3)πr^3. Since the radius of the hemisphere is also 6 cm, we have V_hemisphere = (2/3)π(6^3) = 288π cm^3. Therefore, the exact volume of the frozen yogurt in the cone and hemisphere is 288π cm^3.