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
In a circular garden of radius 15 m, a path of 2 m wide has to be made inside the garden at the rate of ₹ 24 per sq. m. The cost of making the path is: (Take π = \(\frac{22}{7}\) )
A hollow cylinder with outer radius 4 cm and height 2 cm is made up of 1 cm thick metal sheet. What is the volume of metal used? (Take π = \(\frac{22}{7}\))
The length and breadth of a rectangular field are in the ratio 4 : 3. If the cost of cultivating the field at ₹2 per m 2is ₹600, then the length of the field is:
A cylindrical tank has a capacity of 5632 m3. If the diameter of its base is 8 m, what is the depth of the cylindrical tank? (Use π = \(\frac{22}{7}\))
Find the surface area of a sphere whose diameter is equal to 28 cm.
