college math 1012 1

Question

An ice-cream cone has a radius of 2.2 cm and a height of 6.6 cm. The cone is filled with ice-cream and one additional scoop in the shape of a sphere with the same radius as the cone is placed on top. What is the amount of ice cream in cubic cm? Round to the nearest hundredth.

Answer 1

the cone itself, without the topping has volume

= one third height times pi times radius squared

V = 1/3 times h(pi)r^2

= (1/3)6.6(3.14)(2.2)^2

= about 33.45 cm^3

the topping has volume

= the volume of a sphere

= (4/3)pi(r^3) = (4/3)(3.14)(2.2)^3 = 44.60 cm^3

total volume = 33.45 +44.60

= 78.05 cm^3

although a more "normal" ice cream cone would come with half a semi-spherical topping

with 22.3 cm^2 added to 33.45 = 55.75 cm^2 total volume