1.What is the radius of a sphere if its volume and surface area have the same numerical value?
2.A right circular cylinder and a right circular cone share the same radius and volume. What is the ratio of the cylinder's height to the cone's height?
3.A sphere and a right circular cylinder have identical radii, and their volumes are equal. What is the height of the cylinder in terms of its radius?
4.How many solid spheres with a diameter of 6 cm can be formed by melting a solid metal cylinder measuring 45 cm in height and 4 cm in diameter?
5.What is the length of a wire with a radius of 0.2 mm that can be formed by melting a solid copper sphere with a diameter of 18 cm?
6.If the radius of a wire is reduced to one-third of its original size while keeping the volume constant, by what factor will its length change?
7.If the volumes of two cubes are in the ratio 8 to 1, what is the ratio of their side lengths?
8.A metal sheet measuring 27 cm in length, 8 cm in width, and 1 cm in thickness is melted and reshaped into a cube. What is the difference between the surface areas of the original sheet and the resulting cube?
9.A wooden crate measures 8 meters by 7 meters by 6 meters. How many smaller rectangular boxes, each measuring 8 centimeters by 7 centimeters by 6 centimeters, can fit inside this crate at maximum capacity?
10.A cuboid has its length, width, and height in the ratio 6:5:4. If its total surface area measures 33,300 cm², what are the dimensions of the cuboid in centimeters?
11.If a cube has a total surface area of 726 m², what is its volume?
12.Two right circular cones have heights in the ratio 1:2, and the circumferences of their bases are in the ratio 3:4. What is the ratio of their volumes?
13.If the surface areas of two spheres are in the ratio 1 to 4, what is the ratio of their volumes?
14.If the diameters of two spheres are in the proportion 1 to 2, what is the ratio of their volumes?
15.If the diameters of two spheres have a ratio of 1 to 2, what is the ratio of their surface areas?
16.If the edges of two cubes are in the ratio 1:2, what is the ratio of their volumes?
17.A rectangular plot measures 30 meters in length and 20 meters in width. To create a platform measuring 8 meters long, 5.5 meters wide, and 1.5 meters high from the excavated soil, which increases in volume by 10/5 during digging, how deep should the field be dug?
18.How many bricks, each sized 25 cm by 15 cm by 8 cm, are needed to build a wall measuring 10 m in length, 4 m in height, and 5 m in thickness, if 10% of the wall's volume is taken up by mortar?
19.A large box measures 6 meters by 5 meters by 4 meters. If smaller boxes each measuring 60 cm by 50 cm by 40 cm are placed inside, what is the greatest number of smaller boxes that can fit inside the larger box?
20.A brick has dimensions of 20 cm by 10 cm by 7.5 cm. How many such bricks are needed to build a wall measuring 25 m in length, 2 m in height, and 0.75 m in thickness?