# 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. - Mathematics

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.

Concept: Volume of a Cuboid
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 18 Surface Areas and Volume of a Cuboid and Cube
Exercise 18.2 | Q 6 | Page 29

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