Question

Mass-spring-damper systemthe ratio of the curved surface area of two cones, when the diameters of their bases are equal and the slant heights are in the ratio 4:3, is:

a) 9:16
b) 16:9
c) 3:4
d) 4:3

Answer 1

The ratio of the curved surface areas of two cones with equal base diameters and slant heights in the ratio of 4:3 is 16:9.

Step-by-step explanation:

The question is asking to find the ratio of the curved surface areas of two cones, which have equal base diameters while their slant heights are in the ratio of 4:3. The curved surface area of a cone is given by the formula πrl, where r is the radius of the base and l is the slant height of the cone.

Since the diameters are equal, the radii of the cones are also equal. With the slant heights being in the ratio 4:3, we can say l1/l2 = 4/3 (l1 and l2 being the slant heights of the first and second cone, respectively). Because the radii are equal, we can ignore them in our ratio calculation for the surface areas. Thus, the ratio of the curved surface areas of the two cones is directly the square of the ratio of their slant heights, which is (4/3)² = 16/9.

The answer to the question is therefore b) 16:9.