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What is the surface area of a conical grain storage tank that has a height of 37 meters and a diameter of 16 meters? Round the answer to the nearest square meter. A. 2,831 square meters B. 2,664 square meters C. 1,152 square meters D. 1,131 square meters

Bethany Evans

in Mathematics

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Kathy Robinson on October 27, 2018

The surface area of a cone is equal to the base plus the lateral area.The base is a circle and has a diameter of 16 meters.The radius is always half the diameter, so that is 8 metres.The area of a circle = nr2, where r is the radius. π(8)2 = 64π ≈ 201.06193 The area of the base is ≈ 201.06193.To find the lateral area of the cone, we need to find the slant height.From the height, the radius and the slant height of the cone form a right triangle, we can use the Pythagorean Theorem to find the slant height with what we have been given.radius2 + height2 = bias height282 + 372 = bias height264 + 1369 = bias height21433 = bias height2slant height = √1433The lateral area of a cone is equal to the nrl, where r = radius and l = slant height.nrl = π(8)(√1433) ≈ 951.39958(there are other formulas that do the same thing, but no matter).Now we add the lateral area and the base for to find our surface area.201.06193 + 951.39958 = 1152.46151 which is rounded down to C. of 1,152 m2.


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