A scoop of ice cream shape like a sphere with a diameter of 6 cm is placed on an ice cream cone the has a diameter of 5 cm and a height of 9 cm, show that the cone is or is not big enough to hold all of the ice cream when it melts ?

Answer- I said the cone is too small because is volume is smaller than the surface area of the sphere am I correct?

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?

No, your reasoning is not correct. To determine if the cone is big enough to hold all of the ice cream when it melts, we need to compare the volume of the cone with the volume of the sphere.

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

The radius of the cone is half of its diameter, so the radius of the cone is 5 cm/2 = 2.5 cm.

Substituting the values into the formula, we have V_cone = (1/3)π(2.5 cm)^2(9 cm).

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

The radius of the sphere is half of its diameter, so the radius of the sphere is 6 cm/2 = 3 cm.

Substituting the values into the formula, we have V_sphere = (4/3)π(3 cm)^3.

Now, let's calculate the volumes:

V_cone = (1/3)π(2.5 cm)^2(9 cm) ≈ 18.82 cm^3
V_sphere = (4/3)π(3 cm)^3 ≈ 113.1 cm^3

The volume of the cone is smaller than the volume of the sphere. Therefore, the cone is not big enough to hold all of the ice cream when it melts.

To determine whether the cone is big enough to hold all of the ice cream when it melts, we need to compare the volume of the ice cream sphere to the volume of the cone.

First, let's find the volume of the ice cream sphere. The formula for the volume of a sphere is V = (4/3) * π * r³, where r is the radius of the sphere. In this case, the diameter of the sphere is given as 6 cm, so the radius (r) is half of that, which is 3 cm.

Plugging in the values, we have V = (4/3) * π * 3³ = (4/3) * π * 27 = 36π cm³.

Now, let's find the volume of the cone. The formula for the volume of a cone is V = (1/3) * π * r² * h, where r is the radius of the base and h is the height of the cone. In this case, the diameter of the base of the cone is given as 5 cm, so the radius (r) is half of that, which is 2.5 cm. The height (h) of the cone is given as 9 cm.

Plugging in the values, we have V = (1/3) * π * 2.5² * 9 = (1/3) * π * 6.25 * 9 = 18.75π cm³.

Comparing the volumes of the ice cream sphere and the cone, we see that 36π cm³ is greater than 18.75π cm³.

Therefore, the volume of the ice cream sphere is larger than the volume of the cone. This means that the cone is not big enough to hold all of the ice cream when it melts. Thus, your conclusion is correct.

why would you compare volume to surface area? The volumes are

scoop: pi/6 * 6^3 = 113.1 cm^3
cone: pi/12 * 5^2 * 9 = 58.90 cm^3

the cone is too small, but because the volumes compare so.