Question

10 POINTS!!

Suppose a snow cone has a paper cone that is 8 centimeters deep and has a diameter of 5 centimeters. The flavored ice comes in a spherical scoop with a diameter of 5 centimeters and rests on top of the cone. If all the ice melts into the cone, will the cone overflow? Explain.

Answer 1

D

Explanation:

We require to calculate the volume (V) of the cone and sphere.

The volume of a cone is calculated as

V =
`(1)/(3)`πr²h ( r is the radius and h the height )

Here diameter = 5, hence r = 5 ÷ 2 = 2.5, thus

V =
`(1)/(3)`π × 2.5² × 8 ≈ 52.36 cm³

The volume of a sphere is calculated as

V =
`(4)/(3)`πr³ ( r is the radius )

Here diameter = 5, hence r = 5 ÷ 2 = 2.5, thus

V=
`(4)/(3)`π × 2.5³ ≈ 65.45 cm³

Since volume of the sphere is greater than the volume of the cone

Thus when the ice cream melts it will overflow → D