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
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.