1A cone and a cylinder have the same radius of base and the same height. How many times must sand be poured from the cone to fill up the cylinder?
2Is the cylinder filled in three times? What formula for the volume of a cone follows from this?
3What is the shape of the surface of the base of a cone?
4In a cone, what do the symbols l, h and r represent?
5Write the mathematical relationship of l, h and r.
6What is the value of h if l = 13 cm and r = 5 cm?
7Write the curved surface area of a cone if the radius of base is r cm and the slant height is l cm.
8Write the total surface area of a cone in terms of x and y, if the radius of base is x cm and the slant height is y cm.
9What is the volume of a cone if the diameter of base is p cm and the vertical height is q cm?
10Find the volume of a cone if its curved surface area is 81 cm² and its height is 15 cm.
11The total surface area of a cone is 250 cm² and the area of its base is 118 cm². Find its curved surface area.
12Find the volume of a cone if its slant height is 5 cm and the radius of base is 4 cm.
13A cone has base diameter 14 cm and vertical height 21 cm. Find its curved surface area, total surface area and volume.
14A cone has base radius 8 cm and slant height 17 cm. Find its curved surface area, total surface area and volume.
15A cone has vertical height 14 cm and slant height 16 cm. Find its curved surface area, total surface area and volume.
16A cone has slant height 15 cm and base radius 7 cm. Find its curved surface area, total surface area and volume.
17A cone has vertical height 12 cm and base radius 5 cm. Find its curved surface area, total surface area and volume.
18A cone has base diameter 24 cm and vertical height 8 cm. Find its curved surface area, total surface area and volume.
19If the volume of a right circular cone is 100π cm³ and its height is 12 cm, find its slant height.
20Find the radius of base and the height of a conical tent if its volume is 1232 cm³ and the area of its base is 154 cm².
21The amount of plastic needed to make a conical tent with slant height 14 m is 77 m². Find the area and the perimeter of the base of the tent.
22Find the volume, curved surface area and total surface area of a cone with base diameter 8 cm and vertical height 21 cm.
23The vertical height of a solid cone is three times the diameter of its base. Find its total surface area if its volume is 54π cm³.
24A class 10 student made a wooden cone for project work. The area of its base is 154 m² and its height is 14 m. How much does it cost to colour its surface, not including the base, at Rs. 1.50 per square metre?
25A cone-shaped pot is filled with water. Its height is 21 cm and the diameter of its base is 14 cm. When two solid cones of equal size are immersed in it, one third of the water flows out. What is the volume of each cone?
26Three solid cones with the same height and radii 3 cm, 4 cm and 5 cm are melted together and made into one big cone of the same height. Find the diameter of the big cone.
27A conical toy is made of wood and the diameter of its base is 10 cm. It costs Rs. 880 to colour its whole surface at Rs. 4 per square cm. Find the volume of the toy.
28Why does the formula for the volume of a cone have \( \frac{1}{3} \) in it?
29A cone and a cylinder have the same base, but the cone is three times as tall as the cylinder. Compare their volumes.
30Why can the slant height not be used in place of h in the volume formula?
31If the radius of a cone is tripled and its height kept the same, what happens to its volume?