The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.
In this problem, the diameter of the ice cream cone is equal to its height, so let's call the diameter (and height) of the cone D.
The radius of the cone is then D/2.
The volume of the cone is (1/3)π(D/2)^2(D) = (1/3)π(D^3/4).
The volume of the hemisphere on top of the cone is half the volume of a sphere with radius D/2.
The volume of the hemisphere is (1/2)(4/3)π((D/2)^3) = (2/3)π(D^3/8).
To find the total volume of ice cream in and on top of the cone, we add the volume of the cone and the volume of the hemisphere:
Total volume = (1/3)π(D^3/4) + (2/3)π(D^3/8) = [(1/3) + (2/3)(1/2)]π(D^3/4)
= (1/3 + 1/3)π(D^3/4)
= (2/3)π(D^3/4)
Therefore, the total volume of ice cream in and on top of the cone is (2/3)π(D^3/4) cubic units.
Aimee packs ice cream into an ice cream cone. She then puts a perfect hemisphere of ice cream on top of the cone that has a volume of 4 in.3 The diameter of the ice cream cone is equal to its height. What is the total volume of ice cream in and on top of the cone? Use the relationship between the formulas for the volumes of cones and spheres to help solve this problem. Show your work and explain your reasoning. (4 points)
3 answers
Where is the answer and you didn't explain anything you wrote down do it again
Bot?