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Three Metal Cubes with Edges 6 Cm, 8 Cm and 10 Cm Respectively Are Melted Together and Formed into a Single Cube. Find the Volume, Surface Area and Diagonal of the New Cube. - CBSE Class 9 - Mathematics

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Question

Three metal cubes with edges 6 cm, 8 cm and 10 cm respectively are melted together and formed into a single cube. Find the volume, surface area and diagonal of the new cube.

Solution

Let the length of each edge of the new cube be a cm
Then,

`a^3=(6^3+8^3+10^3)cm^3`

`⇒ a^3= 1728`

`⇒ a = 12`

∴ Volume of new cube=`=a^3=1728cm^3`

Surface area of the new cube `6a^2=6xx12^2cm^2`

`= 864 cm^2`

Diagonals of the new cube = `sqrt(3a)= 12 sqrt3cm.`

 

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APPEARS IN

 RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 18: Surface Areas and Volume of a Cuboid and Cube
Ex.18.20 | Q: 6 | Page no. 29
Solution Three Metal Cubes with Edges 6 Cm, 8 Cm and 10 Cm Respectively Are Melted Together and Formed into a Single Cube. Find the Volume, Surface Area and Diagonal of the New Cube. Concept: Volume of a Cuboid.
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