Amy passed ice cream into an ice cream cone she then puts a perfect hemisphere on ice cream of the ice cream on top of the cone that has a volume of 4 inches cubed that diameter of the ice cream cone is equal to its height

Answer 1

To find the volume of the perfect hemisphere, we can use the formula:

V = (2/3) * π * r^3

Since the diameter of the ice cream cone is equal to its height, we can let h be the height of the cone and r be the radius of the hemisphere.

The volume of the cone is given to be 4 inches cubed, so we have:

(1/3) * π * r^2 * h = 4

Since the diameter of the cone is equal to its height, we have:

h = 2r

Substituting this into the volume equation, we get:

(1/3) * π * r^2 * 2r = 4

Multiplying through by 3:

π * r^3 = 12

Simplifying further:

r^3 = 12 / π

Taking the cube root of both sides:

r ≈ 1.565

Now we can find the volume of the hemisphere by substituting the radius into the volume formula:

V = (2/3) * π * (1.565)^3

V ≈ 8.16 inches cubed

So, the volume of the perfect hemisphere is approximately 8.16 inches cubed.