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.
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
1 answer