Calculate the total surface area of a solid cone of slant height 15cm and base radius 8cm in terms of π

The total surface area of a cone is the sum of the curved surface area and the area of the base. The curved surface area of a cone can be found using the formula: πrl where r is the radius of the base and l is the slant height of the cone. The area of the base can be found using the formula: πr² where r is the radius of the base. Given the slant height of the cone as 15cm and base radius as 8cm, we can find the height of the cone using the Pythagorean theorem as follows: height² + 8² = 15² height² + 64 = 225 height² = 225 - 64 height² = 161 height = √161 Therefore, the height of the cone is √161 cm. Now we can find the curved surface area of the cone: πrl = π(8)(√161) = 8π√161 And we can find the area of the base: πr² = π(8)² = 64π The total surface area of the cone is the sum of the curved surface area and the area of the base: total surface area = curved surface area + area of base total surface area = 8π√161 + 64π total surface area = 8π(√161 + 8) Therefore, the total surface area of the cone is 8π(√161 + 8) cm², which is approximately equal to 184π cm². So the answer is (c) 184πcm².