Cook wants to cover the side of a cone shaped funnel with parchment paper to avoid any leaks. The funnel has a diameter of 6 inches in a slant height of
10 inches. The cook wants to find the area of the paper needed to cover the side of the funnel.
To find the area of the paper needed to cover the side of the funnel, we need to find the lateral surface area of the cone.
The lateral surface area of a cone is given by the formula:
L = πrℓ
Where L is the lateral surface area, r is the radius of the base of the cone, and ℓ is the slant height of the cone.
Since the diameter of the base of the cone is 6 inches, the radius (r) is half of that, which is 6/2 = 3 inches.
Plugging in the values into the formula, we have:
L = π(3)(10)
L = 30π square inches
So, the cook will need 30π square inches of parchment paper to cover the side of the funnel.