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Two Cubes Each of Volume 27 Cm3 Are Joined End to End to Form a Solid. Find the Surface Area of the Resulting Cuboid. - CBSE Class 10 - Mathematics

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Question

Two cubes each of volume 27 cm3 are joined end to end to form a solid. Find the surface area of the resulting cuboid. 

Solution

Let the edge of each cube be a cm. 

Volume of each cube = a3 cm3

It is given that the volume of each cube is 27 cm3

∴ a3 = 27= (3)3

⇒ a = 3 

Thus, length of each edge of the cube = 3 cm 

When two cubes are joined end-to-end, the solid obtained is a cuboid whose length, breadth and height are 6 cm, 3 cm and 3 cm respectively. 

This can be diagrammatically shown as follows: 

Surface area of the cuboid = 2 (lb + bh + hl

= 2 (6 cm × 3 cm + 3 cm × 3 cm + 3 cm × 6 cm) 

= 2 × 45 cm2

= 90 cm2

Thus, the surface area of the resulting cuboid is 90 cm2

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Solution Two Cubes Each of Volume 27 Cm3 Are Joined End to End to Form a Solid. Find the Surface Area of the Resulting Cuboid. Concept: Surface Area of a Combination of Solids.
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