Ex.13.1 Q1 Surface Areas and Volumes Solution - NCERT Maths Class 10

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Question

\(2\) cubes each of volume \(64 \;\rm{cm}^3\) are joined end to end. Find the surface area of the resulting cuboid.

 

Text Solution

What is known?

Two cubes each of volume \(64 \;\rm{cm}^3\)  are joined end to end.

What is unknown?

Surface area of the resulting cuboid when two cubes are joined end to end.

Reasoning:

We will find the length of the edge of each cube by using the formula for volume of a cube \(=a^3\) , where length of the edge is \(a. \) 

As the cubes are joined end to end, they will appear as follows

Using the formula for Surface area of a cuboid \(\begin{align} = 2\left( {lb + bh + lh} \right)\end{align}\) ,

where \(l,b\,\,{\rm{ and }}\,\,h\)  are length, breadth and height respectively. We’ll be able to get the answer.

Steps:

Let the length of the edge of each cube is \(a\)
Therefore, volume of the cube \(=a^3\)  

\[\begin{align}\text{volume of the cube,} {a^3} &= 64{c{m^3}}\\{a^3} &= 64{c{m^3}}\\a &= \sqrt[3]{{64c{m^3}}}\\a &= \sqrt[3]{{{{\left( {4{cm}} \right)}^3}}}\\a &= 4{cm}\end{align}\]

Therefore,

Length of the resulting cuboid,\(l = a = 4\rm{cm}\)
Breadth of the resulting cuboid,\(b = a = 4\rm{cm}\)
Height of the resulting cuboid,\(h = 2a = 2 \times 4\rm{cm} = 8\rm{cm}\)

Surface area of the resulting cuboid \( = 2\left( {lb + bh + lh} \right)\)

\[\begin{align}&= 2\left( {4{cm} \times 4{cm} + 4{cm} \times 8{cm} + 4{cm} \times 8{cm}} \right)\\&= 2\left( {16{c{m^2}} + 32{c{m^2}} + 32{c{m^2}}} \right)\\\ &= 2 \times 80{c{m^2}}\\&= 160{c{m^2}}\end{align}\]