Question

Suppose the ice cream on top of a cone makes a perfectly spherical shape. If the diameter of the
ice cream scoop was 6 inches, what will happen to the volume of the ice cream when the ice
cream scoop is decreased to a diameter of 3 inches? What will the original and new volume of
the ice cream be?

Answer 1

The formula for the volume of a sphere is,
\[V=\frac{4}{3}(\pi)r^3\]
Can you go from here?

Answer 2

no

Answer 3

Ok, so the original diameter is 6 inches right? So what is the radius?

Answer 4

V=4/3(3.14)3^3

Answer 5

radius=3

Answer 6

Ok, good. So, you would plug that into the formula.

Also, what class is this for?

Answer 7

Integrated Math II
Unit 8: Geometry of Spheres
Section B: Investigating Changes in Measurement

Answer 8

I got

113.04

Answer 9

Ok, so you are probably going to want to keep your answer in its exact form, or with pi still in the answer.
For this you would take (4/3)(3^3), and then leave pi on the end of the answer. What do you get?

Answer 10

Same answer 113.04

Answer 11

What is (4/3)(3^3)?

Answer 12

volume

Answer 13

It says what is the original and new volume though?

Answer 14

No, I mean literally what is (4/3) multiplied by (3^3)?

Answer 15

36

Answer 16

Ok, so to leave it in its exact form, you would have
\[36\pi\]
That is the original Volume.

Answer 17

ok cool

Answer 18

What about the new volume?

Answer 19

Ok, for the new volume. The diameter is 3, so what is the new radius?

Answer 20

1.5

Answer 21

Ok, so plug that into the equation. What do you get?

Answer 22

4/3(3.14)(1.5^3)

Answer 23

14.3

Answer 24

Ok, be sure to leave it in terms of pi, it makes the last part easier.
Take the original minus the new volume. In terms of pi, what do you get?

Answer 25

98.74

Answer 26

And what do you mean by terms of pi?

Answer 27

Ok, the first answer is
\[36\pi\]
The second part is
\[(\frac{9}{2})\pi\]

Answer 28

That is what I mean by in terms of pi.

Answer 29

Thx for trying

Answer 30

But your answer is kinda wrong

Answer 31

Got to go

Answer 32

Ok. Good luck, if you need help feel free to ask.