A spherical scoop of ice cream is placed on a waffle cone. The

diameter of the ice cream scoop is 6.4 centimeters. The waffle cone has a

diameter of 5 centimeters and a height of 9 centimeters. If all the ice

cream melts before you eat any, how much of the melted ice cream will

overflow the waffle cone? Use 3.14 for pi. Round to the nearest hundredth.

Amount of the melted ice cream that will overflow ≈ 78.31 cm³ (nearest hundredth)

Step-by-step explanation:

To know how much of the ice cream that will overflow the waffle cone we need to calculate the volume of the spherical scoop of ice cream and the volume of the cone.

volume of the spherical scoop of ice cream = 4/3 * πr³

r = 6.4/2 = 3.2 cm

volume of the spherical scoop of ice cream = 4/3 * 3.14 * 3.2³

volume of the spherical scoop of ice cream = 4/3 * 3.14 * 32.768

volume of the spherical scoop of ice cream = 4/3 * 102.89152

volume of the spherical scoop of ice cream = 411.56608 / 3

volume of the spherical scoop of ice cream = 137.188693333

volume of the spherical scoop of ice cream = 137.189 cm³

Volume of the waffle cone = 1/3πr²h

r = 5/2 = 2.5 cm

h = 9 cm

Volume of the waffle cone = 1/3 * 3.14 * 2.5² * 9

Volume of the waffle cone = 1/3 * 3.14 * 6.25 * 9

Volume of the waffle cone = 176.625/3

Volume of the waffle cone = 58.875

Volume of the waffle cone = 58.875 cm³

The amount of the ice cream scoop that will overflow after dissolving will be the volume of the ice cream scoop minus the volume of the waffle cone.

amount that will overflow = 137.189 - 58.875

Amount of the melted ice cream that will overflow = 78.314 cm³

Amount of the melted ice cream that will overflow ≈ 78.31 cm³ (nearest hundredth)