1.A cone has a base radius of 3 cm and a height of 4 cm. What is the volume of this cone?
2.What is the ratio of the curved surface areas of two cylinders with equal heights if their radii are in the ratio 1:2?
3.Two cylinders have equal heights, and their radii are in the ratio 1:3. If the volume of the smaller cylinder is 40 cubic centimeters, what is the volume of the larger cylinder?
4.Calculate the cost of excavating a well that is 14 meters deep with a diameter of 3 meters, if the rate is Rs.15 per cubic meter.
5.A cylinder has a radius of 7 cm and a height of 3 cm. What is the total surface area of this cylinder?
6.A cylindrical container has a diameter of 6 cm and a height of 5 cm. What is the volume of this cylinder?
7.A cylinder has a radius of 2r units and a height of 3r units. What is the curved surface area of the cylinder?
8.A lead sphere with a diameter of 3 cm is melted and reshaped into three smaller spheres. If the diameters of two of these smaller spheres are 1.5 cm and 2 cm, what is the diameter of the third sphere?
9.A solid sphere with a radius of 10 cm is reshaped into 8 smaller solid spheres of identical size. What is the surface area of each smaller sphere (in cm²)?
10.If the surface areas of two spheres have a ratio of 1 to 4, what is the ratio of their volumes?
11.If the volumes of two cubes are in the ratio 27 to 125, what is the ratio of their surface areas?
12.What is the maximum length of a pole that can fit inside a room measuring 12 meters in length, 4 meters in width, and 3 meters in height?
13.Calculate the total length of wire needed to wrap around a square field with an area of 69,696 m² exactly 15 times.
14.Three iron cubes have edges measuring 6 cm, 8 cm, and 10 cm respectively. If these cubes are melted and recast into a single cube, what will be the length of the edge of the new cube?
15.A room has a floor area of 20 m², one longer wall area of 15 m², and a shorter wall area of 12 m². What is the volume of the cube formed using these dimensions as edges?
16.If the edges of two cubes are in the ratio 3 to 1, what is the ratio of their total surface areas?
17.A cuboid has edges measuring 3 cm, 4 cm, and 12 cm. What is the length of its space diagonal?
18.A cuboid has edges measuring 4 cm, 5 cm, and 6 cm. What is the volume of this cuboid?
19.A cuboid has edges measuring 4 cm, 5 cm, and 6 cm. What is its total surface area?
20.Three metal cubes have edges measuring 3 dm, 4 dm, and 5 dm respectively. If these cubes are melted and recast into a single cube, what will be the length of the edge of the new cube?