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 4 inches how many square inches of parchment papers needed to cover the side of the funnel is 3.144 to the nearest hundredth
To find the area of the side of the cone-shaped funnel, we need to calculate the slant height first. The slant height can be found using the Pythagorean theorem:
slant height (l) = √(radius² + height²)
For the smaller end of the funnel:
radius = 2 inches
height = 6 inches
l = √(2² + 6²) = √40 ≈ 6.32 inches
For the larger end of the funnel:
radius = 3 inches
height = 6 inches
l = √(3² + 6²) = √45 ≈ 6.71 inches
The lateral surface area of a cone can be found using the formula:
lateral surface area = π * (radius + slant height)
For the smaller end of the funnel:
lateral surface area = π * (2 + 6.32) ≈ 28.95 square inches
For the larger end of the funnel:
lateral surface area = π * (3 + 6.71) ≈ 33.62 square inches
To find the total square inches of parchment paper needed, we sum up the lateral surface areas of both ends of the cone-shaped funnel:
28.95 + 33.62 ≈ 62.57 square inches
Therefore, approximately 62.57 square inches of parchment paper are needed to cover the side of the funnel.