Three Cuboids of Dimensions 5 Cm × 6 Cm × 7cm, 4cm × 7cm × 8 Cm and 2 Cm × 3 Cm × 13 Cm Are Melted and a Cube is Made. Find the Side of Cube. - Mathematics

Three cuboids of dimensions 5 cm × 6 cm × 7cm, 4cm × 7cm × 8 cm and 2 cm × 3 cm × 13 cm are melted and a cube is made. Find the side of cube.

Solution

$\text { The dimensions of the three cuboids are 5 cm }\times 6 cm \times 7 cm, 4 cm \times 7 cm \times 8 cm \text { and } 2 cm \times 3 cm \times 13 cm .$

$\text { Now, a new cube is formed by melting the given cuboids }.$

$\therefore \text { Voulume of the cube = sum of the volumes of the cuboids }$

$= (5 cm \times 6 cm \times 7 cm) + (4 cm \times 7 cm \times 8 cm) + (2 cm \times 3 cm \times 13 cm)$

$= (210 {cm}^3 ) + (224 {cm}^3 ) + (78 {cm}^3 )$

$= 512 {cm}^3$

$\text { Since volume of a cube = (side ) }^3 , \text { we have }:$

$512 =\text { (side ) }^3$

$\Rightarrow (\text { side) } = \sqrt[3]{512} = 8 cm$

$\therefore \text { The side of the new cube is 8 cm } .$

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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 21.1 | Q 9 | Page 8