If the area of such a surface whose radius is 12cm and whose altitude is 10cm is 240𝜋 cm^2 , what is the area of a similar surface whose radius is 8 cm and whose radius is 9 cm^2

Question

The area of the curved surface of a right circular cylinder varies jointly

as its radius and altitude

Answer 1

The lateral area of a cylinder is 2*PI*R*H. Since the cylinders are similar, the ratio of H ( the height or altitude) will be the same as the ratio of the radii (R).

The ratio of the radii of the cylinder with R = 12 cm to cylinder with R = 8 cm, is 12/8 = 3/2, so ratio of H will be the same and H for 2nd cylinder will be 2/3 * 10 = 6.67 cm and area = 2*PI*8*6.67 = 106.72 PI cm^2.

The ratio of the radii of the cylinder with R = 12 cm to cylinder with R = 9 cm, is 4/3, so ratio of H will be the same and H for 3rd cylinder will be 3/4* 10 = 7.5 cm and area = 2*PI*9*7.5 = 135 PI cm^2.