Question

niko got the jumbo ice cream cone at the Dutchess County Fair. The amount of ice cream can be modeled using a cone whose height is 12 centimeters and radius of 4 cm. A hemisphere and then a full sphere of ice cream the same radius were loaded on top of the cone as shown. If there are 237 cubic centimeters in a cup and 320 calories per cup of ice cream, how many calories is this treat if the cookie cone itself has 85 calories?

Answer 1

There are 897.8 calories in this treat, assuming the cone is filled with ice cream as well.

The formula for the volume of a cone is V=1/3πr²h, and the formula for the volume of a sphere is V=4/3πr³.

For the cone, we have dimensions r = 4 and h = 12:

V=(1/3)(3.14)(4²)(12) = 200.96 cm³.

For the hemisphere, we know that r = 4:
V=(4/3)(3.14)(4³)(1/2) [because it's half of a sphere]
 = 133.97 cm³

The whole sphere will be twice that number, so 

V= 133.97(2) = 267.94

Adding all of these together, we have:

200.96+133.97+267.94 = 602.87cm³

Since there are 237 cm³ in a cup, we divide our total volume by 237:

602.87/237 = 2.54 c

Multiply this by 320 calories per cup:
2.54(320) = 812.8

Add the 85 calories for the cone:
812.8 + 85 = 897.8