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
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 it is 8 meters. The area of a circle = πr², 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. Since the height, radius, and slant height of the cone form a right triangle, we can use the Pythagorean Theorem to find the slant height with what we are given. radius² + height² = slant height² 8² + 37² = slant height² 64 + 1369 = slant height² 1433 = slant height² slant height = √1433 The lateral area of a cone is equal to πrl, where r = radius and l = slant height. πrl = π(8)(√1433) ≈ 951.39958 (there are other formulas which do the same thing, but it doesn't matter.) Now we add the lateral area and base together to find our surface area. 201.06193 + 951.39958 = 1152.46151 which rounds to C. 1,152 m².