MATH SOLVE

5 months ago

Q:
# A snow cone is a tasty treat with flavored ice and a spherical bubble gum ball at the bottom, as shown below: Snow cone with spherical bubble gum ball at the bottom The radius of the cone is 1.5 inches, and its height is 3 inches. If the diameter of the bubble gum ball is 0.5 inches, what is the closest approximation of the volume of the cone that can be filled with flavored ice? 21.21 in3 0.07 in3 7.00 in3 7.07 in3

Accepted Solution

A:

To solve this problem you must apply the proccedure shown below:

1. You have the following information given in the problem above:

- The spherical bubble gum ball is at the bottom

- The radius of the cone is 1.5 inches, and its height is 3 inches.

- The diameter of the bubble gum ball is 0.5 inches.

2. Therefore, you must apply the formula for calculate the volume of a sphere to find the volume of the bubble gum ball:

Vs=4πr^3/3

r is the radius (r=0.5 inches/2=0.25 inches)

Vs=4π(0.25 inches)^3/3

Vs=0.065 inches^3

3. The volume of the cone is:

Vc=πr^2h/3

r is the radius of the cone (r=1.5 inches)

h is the height (h= 3 inches)

Vc=π(1.5 inches)^2(3 inches)/3

Vc=7.06 inches^3

What is the closest approximation of the volume of the cone that can be filled with flavored ice?

Vt=Vc-Vs

Vt≈7.00 inches^3

1. You have the following information given in the problem above:

- The spherical bubble gum ball is at the bottom

- The radius of the cone is 1.5 inches, and its height is 3 inches.

- The diameter of the bubble gum ball is 0.5 inches.

2. Therefore, you must apply the formula for calculate the volume of a sphere to find the volume of the bubble gum ball:

Vs=4πr^3/3

r is the radius (r=0.5 inches/2=0.25 inches)

Vs=4π(0.25 inches)^3/3

Vs=0.065 inches^3

3. The volume of the cone is:

Vc=πr^2h/3

r is the radius of the cone (r=1.5 inches)

h is the height (h= 3 inches)

Vc=π(1.5 inches)^2(3 inches)/3

Vc=7.06 inches^3

What is the closest approximation of the volume of the cone that can be filled with flavored ice?

Vt=Vc-Vs

Vt≈7.00 inches^3