First, we know that the volume of the hemisphere of ice cream on top of the cone is 4 cubic inches. The radius of the hemisphere can be found using the formula for its volume, which gives us a radius of about 1.23 inches. The cone's height and diameter are both about 2.46 inches, so its volume is approximately 3.08 cubic inches. When we add the volume of the cone and the hemisphere together, we get a total volume of about 7.08 cubic inches of ice cream in and on top of the cone.
To find the total volume of ice cream in and on top of the cone, we need to first calculate the volume of the cone. We know that the volume of the perfect hemisphere of ice cream on top is given as 4 cubic inches. The formula for the volume of a hemisphere is
, and if we set this equal to 4, we can solve for
(the radius of the hemisphere). Rearranging gives us
, so
inches. Since the diameter of the hemisphere is 2r, the diameter is about 2.46 inches, meaning the cone also has a diameter of 2.46 inches, giving it a radius of approximately 1.23 inches. The height of the cone is equal to its diameter, so the height is also about 2.46 inches. Now we can calculate the volume of the cone using the formula
. Plugging in our values gives
cubic inches. Now, we add the volume of the cone (approximately 3.08 in³) to the volume of the hemisphere (4 in³), which gives us a total volume of about
cubic inches of ice cream in and on top of the cone.
write in a short 3-4 sentence answer on an 7th grade level
1 answer