Help me figure the surface area of a partial cone please

In summary, the conversation was about measuring the surface area of a concrete structure situated on a drainage canal bank. The speaker provided a sketch with the measured dimensions, but felt that simply averaging and multiplying them was inaccurate. They also tried to stretch it out into a trapezoid, but still didn't feel confident in the accuracy. They mentioned additional dimensions of 32.5' horizontally and 10.5' vertically. They were seeking help for a more accurate measurement method.
  • #1
jonlorio
2
0
I am trying to measure a concrete structure to compute the surface area.
I have included a sketch of the structure with the dimensions that I have measured. This is part of a drainage canal bank where two canals intersect. The banks along both canals are paved with concrete. I tried to just average the slant dimensions and average the lengths of the top and bottom arcs. Then, I simply multiplied them together to get an area. I feel this is inaccurate. I then tried to stretch it out into a trapezoid, but I feel this is even less accurate. Any help?


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  • #2
also, the horizontal dimension is 32.5', and vertical dimension from top to bottom is 10.5' roughly...if that helps any.
 

What is the formula for finding the surface area of a partial cone?

The formula for finding the surface area of a partial cone is SA = πrl + πr², where r is the radius of the base and l is the slant height of the cone.

Can you explain the terms "radius" and "slant height" in the formula?

The radius is the distance from the center of the circle to the edge of the base, while the slant height is the distance from the tip of the cone to any point on the edge of the base.

What is the unit of measurement for surface area?

The unit of measurement for surface area is typically square units, such as square inches, square feet, or square meters.

Can the surface area of a partial cone be negative?

No, the surface area of a partial cone cannot be negative. It is always a positive value, representing the total area of the curved surface and base of the cone.

Is there a specific order in which the numbers should be plugged into the formula?

Yes, there is a specific order in which the numbers should be plugged into the formula. The radius should be plugged in first, followed by the slant height, and then any other necessary numbers, such as the value of π.

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