Question

The first ice cream cone was made at the World’s Fair in St. Louis in 1904 when an ice cream seller ran out of cups. Suppose a sugar cone for ice cream is 10cm deep and has a diameter of 4cm. A scoop of ice cream with a diameter of 4cm rests on top of the cone. If all the ice cream melts into the cone, will the cone overflow?

Answer 1

volume of cone: pi x r^2 x H/3
3.14 x 2^2 x 10/3 = 41.87 cubic cm

volume of ice cream: 4/3 x pi x R^3
4/3 x 3.14 x 2^3 = 33.49 cubic cm

volume of cone is larger than volume of ice cream so no it will not overflow