Volume of a Cube, Volume of a Cuboid
A rectangular container, whose base is a square of side 5 cm, stands on a horizontal table, and holds water up to 1 cm from the top. When a cube is placed in the water it is completely submerged, the water rises to the top and 2 cubic cm of water overflows. Calculate the volume of the cube and also the length of its edge.
A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.
A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?
How many cubic centimeters of iron are there in an open box whose external dimensions are 36 cm, 25 cm and I 6.5 cm, the iron being 1.5 cm thick throughout? If I cubic cm of iron weighs 15g, find the weight of the empty box in kg.
A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?
The dimensions of a cinema hall are 100 m, 50 m and 18 m. How many persons can sit in the hall, if each person requires 150 `m^3` of air?