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?

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