To find the volume of the frozen yogurt cone, we first need to find the volume of the cone and the hemisphere separately, and then add them together.
The volume of a cone is given by the formula:
V_cone = (1/3) * π * r^2 * h_cone
where r is the radius of the cone and h_cone is the height of the cone.
Substituting the given values, we have:
V_cone = (1/3) * π * (6)^2 * 24
= (1/3) * π * 36 * 24
= (1/3) * π * 864
= 288π
The volume of a hemisphere is given by the formula:
V_hemisphere = (2/3) * π * r^3
Substituting the given radius, we have:
V_hemisphere = (2/3) * π * (6)^3
= (2/3) * π * 216
= 144π
Therefore, the volume of the frozen yogurt in the cone and hemisphere is:
V_total = V_cone + V_hemisphere
= 288π + 144π
= 432π
So the exact volume of the frozen yogurt in the cone and hemisphere is 432π cubic cm.
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.
1 answer