A cook wants to cover the side of a cone-shaped funnel with parchment paper to avoid any leaks or spills. The funnel has a diameter of 6 inches and a slant height of 4 inches. How many square inches of parchment paper is needed to cover the side of the funnel? Use 3.14 for pi and round your answer to the nearest hundredth. (1 point)

Question

Create an image depicting a cooking scenario where a Caucasian male cook is trying to cover the side of a cone-shaped funnel with a piece of parchment paper. The funnel, placed on a kitchen counter besides some freshly made dough, is about 6 inches in diameter and has a slant height of about 4 inches. The image should not contain any numerical values or text. Colour the parchment paper tan, the dough white, the funnel metal-grey and the kitchen counter in brown wood texture.

A cook wants to cover the side of a cone-shaped funnel with parchment paper to avoid any leaks or spills. The funnel has a diameter of 6 inches and a slant height of 4 inches. How many square inches of parchment paper is needed to cover the side of the funnel? Use 3.14 for pi and round your answer to the nearest hundredth. (1 point)

Answer 1

The answers 37.68 square with inches.

You’re welcome.

Answer 2

The circumference of the base of the cone can be found using the formula C = pi * d, where C is the circumference and d is the diameter.

C = 3.14 * 6 = 18.84 inches.

The slant height of the cone forms the hypotenuse of a right triangle with the radius of the base as the other leg. Using the Pythagorean theorem, we can find the radius:
r^2 = s^2 - h^2
r^2 = 6^2 - 4^2
r^2 = 36 - 16
r^2 = 20
r = sqrt(20) = 4.47 inches (rounded to the nearest hundredth).

Now we can find the length of the cone side by finding the circumference of the base (18.84 inches) times the slant height of the cone (4 inches):
length = circumference * slant height
length = 18.84 * 4 = 75.36 inches.

Therefore, approximately 75.36 square inches of parchment paper is needed to cover the side of the funnel.