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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 1.25 inches, and its height is 2.75 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? (4 points)

Group of answer choices

4.43 in3

0.07 in3

13.50 in3

4.50 in3

Respuesta :

Answer:  Choice A) 4.43 in^3

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Explanation:

The volume of the cone is...

V = (1/3)*pi*r^2*h

V = (1/3)*3.14*(1.25)^2*2.75

V = 4.49739583333333

which is approximate.

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The volume of the sphere is

V = (4/3)*pi*r^3

V = (4/3)*3.14*(0.25)^3 ... note the radius is half the diameter

V = 0.06541666666667

which is approximate as well

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Subtract the two volumes to finish things up

4.49739583333333-0.06541666666667 = 4.43197916666667

The result 4.43197916666667 then rounds to 4.43

This is the approximate amount of empty space in the cone that isn't taken up by the spherical gum. The units are in "cubic inches" or "in^3" for short.