The volume of a cone is 8192 π cm³. The height of the cylinder is 35% more than the slant height of the cone. The lateral surface area of the cylinder is 4536 π cm². If the base area of the cone is 1024 π cm², then find out the volume of the cylinder (in  cm ³).

Solution

If the base area of the cone is 1024 π cm².  π x (radius of the cone)² = 1024 π     Eq.(i) radius of the cone = 32 cm [Here negative value is not possible.] The volume of a cone is 8192 π cm³. (⅓) x π x (radius of the cone)² x height of the cone = 8192 π Put Eq.(i) in the above equation. (⅓) x height of the cone = 8 height of the cone = 24 cm    Eq.(ii) (slant height of the cone)² = (radius of the cone)² + (height of the cone)² (slant height of the cone)² = (32)² + (24)² = 1024+576 = 1600 slant height of the cone = 40 cm The height of the cylinder is 35% more than the slant height of the cone. height of the cylinder = (100+35)% of 40 height of the cylinder = 135% of 40 = 54 cm The lateral surface area of the cylinder is 4536 π cm². 2 x π x radius of the cylinder x height of the cylinder = 4536 π radius of the cylinder x 54 = 2268 radius of the cylinder = 42 Volume of the cylinder = π x (radius of the cylinder)² x height of the cylinder = π x (42)² x 54 = (22/7) x 1764 x 54 = 22 x 252 x 54 = 299376 cm³