The radius of the cone is 1.75 inches, and its height is 3.5 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)

Option A. 11.15 in³

Step-by-step explanation:

The question is as following:

A snow cone is a tasty treat with flavored ice and a spherical bubble gum ball at the bottom. The radius of the cone is 1.75 inches, and its height is 3.5 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?

A.) 11.15 in³

B.) 11.22 in³

C.) 0.07 in³

D.) 33.67 in³

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Solution:

Volume of the cone = π r² h/3

Vcone = 3.14 * (1.75in)² * 3.5in/3

Vcone = 3.14 * 3.0625 in² * 1.167

Vcone = 11.22 in³

Volume of the gum ball = 4/3 * π * r³

Vball = 4/3 * 3.14 * (0.5in/2)³

Vball = 4/3 * 3.14 * (0.25in)³

Vball = 4/3 * 3.14 * 0.015625 in³

Vball = 0.065 in³

11.22 in³ - 0.065 in³ = 11.155 in³  

The answer is option A. 11.15 in³

true

step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1