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Show that the Product of the Areas of the Floor and Two Adjacent Walls of a Cuboid is the Square of Its Volume. - Mathematics

Answer in Brief

Show that the product of the areas of the floor and two adjacent walls of a cuboid is the square of its volume.

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Solution

\[\text { Suppose that the length, breadth and height of the cuboidal floor are l cm, b cm and h cm, respectively . } \]

\[\text { Then, area of the floor = l } \times b {cm}^2 \]

\[\text { Area of the wall = b } \times h {cm}^2 \]

\[\text { Area of its adjacent wall = l  }\times h {cm}^2 \]

\[\text { Now, product of the areas of the floor and the two adjacent walls  }= (l \times b) \times (b \times h) \times (l \times h) = l^2 \times b^2 \times h^2 = (l \times b \times h )^2 \]

\[\text { Also, volume of the cuboid = l } \times b \times h {cm}^2 \]

\[ \therefore\text {  Product of the areas of the floor and the two adjacent walls } = (l \times b \times h )^2 = \text { (volume  })^2\]

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APPEARS IN

RD Sharma Class 8 Maths
Chapter 21 Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube)
Exercise 21.3 | Q 13 | Page 22
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