## Cuboid1) volume of cuboid = l × b × h. Since l × b is the area of its base we can also say that,Volume of cuboid = area of the base × height. ## Cube1) The cube is a special case of a cuboid, where l = b = h.Hence, volume of cube = l × l × l = l ^{3}## Cylinder1) Volume of cylinder = area of base × height = πr^{2} × h = πr^{2}h.## Volume and CapacityThere is not much difference between these two words.(a) Volume refers to the amount of space occupied by an object. (b) Capacity refers to the quantity that a container holds. ## Example 1:Find the height of a cuboid whose volume is 275 cu. cm and base area is 25 sq. cm . ## Solution:Volume of a cuboid = Base area × Height Hence height of the cuboid = Volume of cuboid/Base area = 275/25 = 11 cm Height of the cuboid is 11 cm. ## Example 2:A godown is in the form of a cuboid of measures 60 m × 40 m × 30 m. How many cuboidal boxes can be stored in it if the volume of one box is 0.8 cu. m ? ## Solution:Volume of one box = 0.8 cu. m Volume of godown = 60 × 40 × 30 = 72000 cu. m Number of boxes that can be stored in the godown = Volume of the godown / Volume of one box =60 × 40 × 30 / 0.8 = 90,000 Hence the number of cuboidal boxes that can be stored in the godown is 90,000. ## Example 3:A rectangular paper of width 14 cm is rolled along its width and a cylinder of radius 20 cm is formed. Find the volume of the cylinder. ## Solution:A cylinder is formed by rolling a rectangle about its width. Hence the width of the paper becomes height and radius of the cylinder is 20 cm. Height of the cylinder = h = 14 cm Radius = r = 20 cm Volume of the cylinder = V = π ^{2}h = π × 20 × 20 × 14 = 17600 cu. cmHence, the volume of the cylinder is 17600 cu. cm. ## Example 4:A rectangular piece of paper 11 cm × 4 cm is folded without overlapping to make a cylinder of height 4 cm. Find the volume of the cylinder. ## Solution:Length of the paper becomes the perimeter of the base of the cylinder and width becomes height. Let radius of the cylinder = r and height = h Perimeter of the base of the cylinder = 2πr = 11 or r = 7/4 cm Volume of the cylinder = V = πr ^{2}h = π × (7/4)×(7/4)× 4 cu. cm = 38.5 cu. cm.Hence the volume of the cylinder is 38.5 cu. cm. ## Read MoreSurface Area of Cube Cuboid Cylinder |