Question 8 Volume Surface Area Cuboid Cube Exercise 21.1
Let us consider,
Length of a cuboid be ‘l’
Breadth of a cuboid be ‘b’
Height of a cuboid be ‘h’
So, Volume of a cuboid = l × b × h
(i) Length of a cuboid becomes = 2l
Breadth = b/2
Height = h
Volume of cuboid = 2l × b/2 × h = l × b × h (remains same)
(ii) Length of a cuboid becomes = 2l
Breadth = b
Height = 2h
Volume of cuboid = 2l × b × 2h = 4lbh (four times)
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Cuboid is a three-dimensional solid object. It is also referred to as a regular hexahedron and is one of the five platonic solids. All the edges share at least a common edge with each other. The structure of a cuboid can be defined in terms of the fact that each of the faces is being connected to four vertices and four edges, vertex connected with three edges and three faces, and edges are in touch with two faces and two vertices. The length, breadth, or height may or may not be equal in the case of a cuboid.
Properties of Cuboid
Volume of Cuboid
The volume of a cuboid is equivalent to the amount of space occupied within the figure. The volume of any three-dimensional figure is dependent on the three edges’ length, that is, its length, breadth, and height. It can be considered to be a solid rectangle. Let us assume the height of the cuboid to be h, l its length and breadth to be denoted by b units respectively.
In addition to this, let us assume V to be the volume of the cuboid. Deriving its formula,
The volume of cuboid = Base area × Height
The base area for cuboid = l × b
Volume of the cuboid = Area of cuboid × Height
What will happen to the volume of a cuboid if its length is doubled, height is the same, and breadth is halved?
Question 1. If volume of a cuboid is 24000 cm3. Then find the change in the volume if its length is doubled, height is the same and breadth is halved?
Question 2. If the volume of the cuboid is 3000 m3 and its length is 20 m breadth is 15 m, then find the height of the cuboid?
Question 3. Consider the length of a cuboid is double its breadth, breadth of cuboid is double of its height, and volume of the cuboid is 8000 m3. Find all the dimensions of the cuboid?
Question 4. Assume that the breadth of the cuboid is halved, then find how much the volume of cuboid changes?
Question 5. Calculate the amount of water in m3 that can be filled in a water tank of length 50 m breadth 40 m and height 10 m?