Asked by XavionFrost77

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. Make it simple.
Answered by XavionFrost77
Shorter plz.
Answered by XavionFrost77
Can you make it 125 Words plz.
Answered by girlyy
To find the total volume of ice cream in and on top of the cone, we need to calculate the volume of both the cone and the hemisphere of ice cream and then add them together.

The volume of a cone is given by the formula V = (1/3) * π * r^2 * h, where V represents volume, π is a constant (approximately 3.14), r is the radius of the base of the cone, and h is the height of the cone.

Since the diameter of the cone is equal to its height, we can say that the radius of the cone is half of the diameter.

The volume of a hemisphere is given by the formula V = (2/3) * π * r^3.

Given that the hemisphere of ice cream has a volume of 4 in³, we can use the formula to find the radius of the hemisphere.

By rearranging the formula, we have r^3 = (3 * 4) / (2 * π).

Solving for r, we find that the radius of the hemisphere is approximately 1.113.

Since the diameter and height of the cone are the same, the radius of the cone is also approximately 1.113.

Now, we can calculate the volume of the cone using the formula V = (1/3) * π * r^2 * h.

Substituting the values, we find that the volume of the cone is approximately 1.548 in³.

Therefore, the total volume of ice cream in and on top of the cone is approximately 1.548 + 4 = 5.548 in³.
There are no AI answers yet. The ability to request AI answers is coming soon!