1.If the volumes of two cubes are in the ratio 8 to 1, what is the ratio of their side lengths?
2.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?
3.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?
4.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?
5.If a cube has a total surface area of 726 m², what is its volume?
6.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?
7.If the surface areas of two spheres are in the ratio 1 to 4, what is the ratio of their volumes?
8.If the diameters of two spheres are in the proportion 1 to 2, what is the ratio of their volumes?
9.If the diameters of two spheres have a ratio of 1 to 2, what is the ratio of their surface areas?
10.If the edges of two cubes are in the ratio 1:2, what is the ratio of their volumes?
11.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?
12.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?
13.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?
14.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?
15.What is the volume of soil removed when excavating a pond measuring 20 meters in length, 10 meters in width, and 5 meters in depth?
16.If the height of a cone is doubled, by what percentage does its volume increase?
17.A cone and a cylinder share the same base radius and height. What is the ratio of the volume of the cylinder to the volume of the cone?
18.What is the maximum length of a rod that can be placed inside a cube-shaped room with each side measuring 4 meters?
19.What is the total surface area in square centimeters of a cardboard box measuring 25 cm by 15 cm by 8 cm?
20.A rectangular tank measuring 3 meters in length, 2 meters in width, and 1.5 meters in depth is excavated in a field that is 20 meters long and 14 meters wide. If the soil removed from the tank is uniformly spread over the entire field, by approximately how many centimeters will the field's surface level rise?