Question

Q23) A cubold is 40 cm x 20 cm x 10 cm What would be the side of a cube having the
same volume?​

Answer 1

$\underline{ \underline{ \Large \pmb{\mathit{ {Given:}} }} }$

• Length of cuboid = 40 cm

• Breadth of cuboid = 20 cm

• Height of cuboid = 10 cm

$\underline{ \underline{ \Large \pmb{\mathit{ {To \: calculate :}} }} }$

• What would be the side of a cube having the same volume?

$\underline{ \underline{ \Large \pmb{\mathit{ {Clarification :}} }} }$

Here, we are given the dimensions of the cuboid i.e, length , breadth and height are 40 cm , 20 cm and 10 cm. Then, it is asked to us that what would be the side of a cube having the same volume as the cuboid. So, at first we'll calculate the volume of the cuboid and then we'll form an algebraic equation and by solving that equation, we'll find the side of the cube having the same volume as the cuboid.

$\underline{ \underline{ \Large \pmb{\mathit{ {Explication \: of \: steps :}} }} }$

According to the question,

As per the given question the volume of cuboid and the volume of cube is same.

$\bigstar \: \boxed{\sf { {Volume}_{(Cuboid)} = {Volume}_{(Cube)} }}$

V O L U M E⠀O F⠀ C U B O I D :

$\longrightarrow \sf { {Volume}_{(Cuboid)} = \ell \times b \times h }$

• $\ell$ denotes length.
• b denotes breadth.
• h denotes height.

$\longrightarrow \sf { {Volume}_{(Cuboid)} = 40 \: cm \times 20 \: cm \times 10 \: cm }$

$\longrightarrow \sf { {Volume}_{(Cuboid)} = (40 \times 20 \times 10) \: {cm}^{3} }$

$\longrightarrow \sf { {Volume}_{(Cuboid)} = (800 \times 10) \: {cm}^{3} }$

$\longrightarrow \underline{\boxed{ \sf { {Volume}_{(Cuboid)} = 8000 \: {cm}^{3} }} } \: \red{\bigstar}$

So, substituting the value of volume of cuboid in the equation given below :-

$\bigstar \: \boxed{\sf { {Volume}_{(Cuboid)} = {Volume}_{(Cube)} }}$

$\longrightarrow \sf {8000 \: {cm}^{3} = Volume_{Cube} }$

$\longrightarrow \sf {8000 \: {cm}^{3} = {a}^{3} }$

Where,

• a = Side of the cube.

It is a variable in the above equation that we need to find.

$\longrightarrow \sf {8000 \: {cm}^{3} = {a}^{3} }$

$\longrightarrow \sf { \sqrt[3]{8000 \: {cm}^{3} } = a}$

$\longrightarrow \sf { 20 \: cm = a}$

$\longrightarrow \underline{\boxed{ \sf { {Side}_{(Cube)} = 20 \: cm }} } \: \green{\bigstar}$

Therefore, side of the cube is 20 cm which has same volume as the cuboid having dimensions of 40 cm × 20 cm × 10 cm.

Answer 2

Answer:

Dimensions of the cuboid = $\it 40 \ cm \times 20 \ cm \times 10 \ cm$

Let the side of the cube be = $\it (s) \ cm$

We know, $\it V_{cube} = a^3$ and $\it V_{cuboid} = lbh$

As per condition,

$\it V_{cube} = V_{cuboid}$

⇒ $\it s^3 = 40 \times 20 \times 10$

⇒ $\it s = \sqrt[3]{40 \times 200}$

⇒ $\it s = \sqrt[3]{(20^3)}$

⇒ $\it s = 20$.

∴ Side of the cube measures $\it 20 \ cm$.