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4. Rectangular Parallelopiped or Cuboid
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Q24 of 35 Page 74

If the total surface area of a cube is s sq. unit and the length of the diagonal is d unit, then the relation between s and d is

Let the edge be of a cm


then total surface area of cube = s = 6a2


a =


and body diagonal = d = 3a


a =


Thus,


Squaring both sides,



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24

The surface area of cube is 256 sq. m, the volume of the cube is

24

The ratio of volume of 2 cubes is 1:27, the ratio of total surface areas of 2 cubes are

24

Let us write true/false of the following statements:

(i) If the length of each of a cube is twice of that 1st cube then the


volume of this cube is 4 times more than that of the 1st cube.


(ii) In rainy season, the height of rainfall in 2 hectare land is 5 cm, the volume of rain water is 1000 cubic metre.


[hint: 1 are = 100 sq. m,1 hectre = 100are]

24

Let us fill in the blanks:

(i) The number of diagonals of a cuboid is ________.


(ii) The length of diagonal on the surface of a cube = ________× the length of one edge.


(iii) If the length, breadth and height of a rectangular parallelepiped are equal, then the special name of this solid is _________.

Questions · 35
4. Rectangular Parallelopiped or Cuboid
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