A scoop of ice cream, shaped like a sphere with a diameter of 6 cm, is placed in an ice cream cone with a diameter of 5cm and a height of 9 cm. Is the cone big enough to hold all the ice cream if it melts? Explain.

Question

anonymous · Answer

The amount of ice cream when it's frozen is the same as when it is melted. 

so that means if we can find the volume of the sphere, we can compare it to the volume of the cone, and see if it is less than the cone's volume.

Can you find the volume of the sphere of ice cream for me?

anonymous · Answer

$$V Sphere = 4/3\pi r^3$$ and 

Volume of a Cone = $$h/3 * \pi r^2$$

Remember to divide your diameter by 2 to get the radius of each of the shapes before plugging into the formulas. Compare the volumes of each to see if the cone is greater than or equal to the sphere.

anonymous · Answer

okay well can you help me through the problem

anonymous · Answer

first find the volume of the sphere by figuring out the radius of the ice cream

anonymous · Answer

I need help finding the radius

anonymous · Answer

Your diameter is 6 so if you divide by 3 your radius is 3

anonymous · Answer

okay well I need help with this whole problem can you just walk me through it?

anonymous · Answer

Plug in $$4/3 \pi 3^3$$ This will give you your volume of the sphere

anonymous · Answer

Approximately 113

anonymous · Answer

Now you need to know your volume of the cone so find the radius of the base of the cone by dividing the diameter by 2.

anonymous · Answer

Knowing your height of 9 and a diameter of 5 you should plug in to the cone formula and get $$9/3 * 3.14*2.5^2$$

anonymous · Answer

This will be approximately 58.8 so, no the cone will not hold the ice cream if it all melts.