An ice cream cone is 11 cm deep and 5 cm across the opening of the cone. Two hemisphere-shaped scoops of ice cream, which also have diameters of 5 cm, are placed on top of the cone. If the ice cream were to melt into the cone, would it overflow?

Respuesta :

Answer:

The melted ice cream would overflow.

Step-by-step explanation:

Volume of the cone = 1/3 π r^2 h

= 1/3 * 11 * 2.5^2  π

= 22.917 π  cm^3.

Volume of the 2 scoops = 2 * 4/3  π  r^3

= 8/3 * 2.5^3  π

= 41.67 π  cm^3  -  which is greater than the volume of the cone.

So the ice cream would overflow.

Based on the volume of the cone and the volume of the ice cream, there would not be overflow.

Would there be an overflow?

In order to determine if there would be an overflow, the volumes of the cone and the ice creams have to be determined.

Volume of a cone = 1/3(nr^2h)

n = 22/7

r = radius - 5/2 = 2.5cm

h = height

1/3 x 22/7 x 11 x 2.5^2 = 72.02

Volume of the hemisphere = 2 x [(2/3) x (n) x (r^3)]

n = 22/7

r = radius

2 x [2/3 x 22/7 x 2.5^2) = 65.48

To learn more about the volume of a cone, please check: https://brainly.com/question/13705125