an ice cream cone contains one spherical scoop of ice cream,the diameter of the scoop of ice cream is the same as the diameter of the cone. If the ice cream melts, will the cone overflow? Justify your answer.

4cm spherical scoop of ice cream

diameter of cone- 7cm

contradiction:

you say the diameter of the cone is the same as the diameter of the ice crream, but then you say
4 cm scoop of ice cream vs 7 cm of diameter of cone

To determine whether the melted ice cream will overflow the cone, we need to compare the volume of the ice cream scoop to the volume of the cone.

First, let's calculate the volume of the scoop of ice cream.

The formula for the volume of a sphere is given by V = (4/3)πr^3, where "V" is the volume and "r" is the radius of the sphere.

Given that the diameter of the scoop is 4 cm, the radius (r) can be calculated as half of the diameter, which is 2 cm. Plugging this value into the formula, we get:

V_ice cream = (4/3)π(2^3)
= (4/3)π(8)
= (32/3)π cm^3

Now, let's calculate the volume of the cone.

The formula for the volume of a cone is V = (1/3)πr^2h, where "V" is the volume, "r" is the radius of the base, and "h" is the height of the cone.

Given that the diameter of the cone is 7 cm, the radius (r) can be calculated as half of the diameter, which is 3.5 cm. The height (h) of the cone will depend on the length of the ice cream scoop.

Since the diameter of the scoop of ice cream is the same as the diameter of the cone, when the ice cream is placed on top of the cone, it will fill the cone. Therefore, the height of the cone will be equal to the diameter of the scoop, which is 4 cm.

Plugging these values into the formula, we get:

V_cone = (1/3)π(3.5^2)(4)
= (1/3)π(12.25)(4)
= (1/3)π(49)
= (49/3)π cm^3

Now, let's compare the volumes of the ice cream scoop and the cone:

V_ice cream = (32/3)π cm^3
V_cone = (49/3)π cm^3

Since the volume of the cone is greater than the volume of the ice cream scoop, when the ice cream melts, it will not overflow the cone. There will be enough space for the melted ice cream to fill the cone without overflowing.