you have a scoop of ice cream 3 inches in diameter sitting on a cone with 1 inch
What is your question? One inch of what?
yes
To calculate the volume of the ice cream scoop, we can use the formula for the volume of a sphere:
V = (4/3) * π * r^3
where V is the volume and r is the radius of the sphere (which is half its diameter).
In this case, the diameter of the ice cream scoop is 3 inches, so the radius is 3/2 = 1.5 inches.
Plugging this value into the formula, we get:
V = (4/3) * π * (1.5)^3
Now, let's calculate the volume of the ice cream scoop using this formula:
V = (4/3) * 3.14 * (1.5)^3
= (4/3) * 3.14 * 3.375
≈ 14.14 cubic inches (rounded to two decimal places)
So, the volume of the ice cream scoop is approximately 14.14 cubic inches.
As for the cone, we can calculate its volume using the formula for the volume of a cone:
V = (1/3) * π * r^2 * h
where V is the volume, r is the radius of the cone's base, and h is the height of the cone.
In this case, the radius of the cone's base is 1 inch, and the height of the cone is unknown. However, we know that the height of the entire scoop, including the cone, is 4 inches (3 inches for the scoop and 1 inch for the cone).
To find the height of the cone, we subtract the height of the scoop from the total height:
Height of the cone = Total Height - Height of the Scoop
= 4 inches - 3 inches
= 1 inch
Now we have the values for the radius (1 inch) and the height (1 inch) of the cone. Let's calculate the volume of the cone using the formula:
V = (1/3) * 3.14 * (1)^2 * 1
= (1/3) * 3.14 * 1
≈ 1.047 cubic inches (rounded to three decimal places)
The volume of the cone is approximately 1.047 cubic inches.
So, when combined, the ice cream scoop and the cone have a total volume of approximately 14.14 cubic inches (scoop) + 1.047 cubic inches (cone) ≈ 15.187 cubic inches.