A right circular cone and a right circular cylinder have equal base radius and equal height. If the radius of base and height are in the ratio 5:125:12, find the ratio of the total surface area of the cylinder to that of cone.3:13:113:913:917:917:934:934:9

The total surface area of a right circular cylinder is given by the formula 2πr(h + r), where r is the radius of the base and h is the height.

The total surface area of a right circular cone is given by the formula πr(l + r), where r is the radius of the base, l is the slant height, and h is the height.

Given that the radius and height are in the ratio 5:12, we can substitute these values into the formulas. However, we need to find the slant height (l) for the cone. We can do this using the Pythagorean theorem, since the radius, height, and slant height of a cone form a right triangle.

The Pythagorean theorem is a² + b² = c². In this case, a is the radius (5), b is the height (12), and c is the slant height (l). Solving for l, we get l = √(5² + 12²) = √169 = 13.

Substituting these values into the formulas, we get:

Total surface area of cylinder = 2π(5)(12 + 5) = 170π Total surface area of cone = π(5)(13 + 5) = 90π

Therefore, the ratio of the total surface area of the cylinder to that of the cone is 170π : 90π = 17 : 9.