A right circular cone of height h and radius R is cut by a plane parallel to the base at a distance h/4 from the base. The ratio of the curved surface areas of the resulting cone to the frustum is:
9 : 7
Height of the smaller cone = h - (h/4) = (3h/4)
By similarity, ratio of radii = (3h/4) : h = 3:4
Curved surface area (CSA) ratio of smaller cone to original cone = (3²) : (4²) = 9:16
CSA of frustum = CSA of original cone - CSA of smaller cone
Ratio of smaller cone to frustum = 9 : (16 - 9) = 9 : 7
Thus, the correct answer is 9 : 7.
Important Questions from Mensuration
The areas of three adjacent faces of a cuboidal tank are 3 m 2, 12 m 2 and 16 m 2. the capacity of the tank, in litres, is:
Volume of a cuboid is 4800 cm 3. If the height of this cuboid is 20 cm, then what will be the area of the base of cuboid ?
Two similar cubes have heights of 8 cm and 12 cm, respectively. If the capacity of the smaller cube is 80 cm 3, what is the capacity of the bigger cube (in cm 3)?
Three circles of radius 7 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
Three circles of radius 6 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
