1.A cylinder has a radius of 2r units and a height of 3r units. What is the curved surface area of the cylinder?
2.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?
3.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)?
4.If the surface areas of two spheres have a ratio of 1 to 4, what is the ratio of their volumes?
5.If the volumes of two cubes are in the ratio 27 to 125, what is the ratio of their surface areas?
6.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?
7.Calculate the total length of wire needed to wrap around a square field with an area of 69,696 m² exactly 15 times.
8.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?
9.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?
10.If the edges of two cubes are in the ratio 3 to 1, what is the ratio of their total surface areas?
11.A cuboid has edges measuring 3 cm, 4 cm, and 12 cm. What is the length of its space diagonal?
12.A cuboid has edges measuring 4 cm, 5 cm, and 6 cm. What is the volume of this cuboid?
13.A cuboid has edges measuring 4 cm, 5 cm, and 6 cm. What is its total surface area?
14.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?
15.How many smaller cubes with edges measuring 2 decimeters can be obtained from a cube with a 1-meter edge?
16.A cube has a volume of 1728 cubic centimeters. What is the total surface area of this cube?
17.If the total surface area of a cube is 24 square centimeters, what is the volume of the cube?
18.If the side length of a cube measures 2a cm, what is the total surface area of the cube?
19.A solid is formed by placing a right circular cone perfectly on top of a circular cylinder. The cone has a height of h. If the combined volume of the solid is three times the volume of the cone alone, what is the height of the cylinder?
20.By what percentage does the volume of a sphere increase when its radius is doubled?