Question

The number of planks of dimensions 5m×25cm×10cm that can be placed in a pit which is 20m long ,6 m wide and 80cm deep is

Answer 1

$\sf \underline{ \underline{Question :}}$

How many planks of dimensions (5m × 25cm × 10cm) can be stored in a pit which is 20m long, 6m wide and 80cm deep?

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$\sf \underline{ \underline{ Given:}}$

• Dimensions of the plank = (5m × 25cm × 10cm)
• Dimensions of the pit = (20m × 6m × 80cm)

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$\sf \underline{ \underline{ To \: Find:}}$

• Number of planks = ?

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$\sf \underline{ \underline{ Solution:}}$

~ Formula Used :

$\sf \pink{⇢} \: \: \small{\underline{{\boxed{\sf{\purple{ \: \: Volume = Length × Breadth × Height }}}}}}$

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~ Noting the dimensions of the plank :

• ➳ Length = 5m = 500 cm
• ➳ Breadth = 25 cm
• ➳ Height = 10 cm

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~ Substituting the values :

$\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⟼ \: \: \: \: \: \: \: \: Volume \: of \: the \: plank = (500 × 25 × 10) cm³}$

$\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⟼ \: \: \: \: \: Volume _{(plank)} \: = \green{125000 {cm}^{3}} }$

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~ Noting the dimensions of the pit :

• ➳ Length = 20m = 2000 cm
• ➳ Breadth = 6m = 600 cm
• ➳ Height = 80 cm

We know that :

$\sf \pink{⇢} \: \: \small{\underline{{\boxed{\sf{\purple{ \: \: Volume _{(pit)} = Length × Breadth × Height }}}}}}$

By substituting the values :

$\sf{{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⟼ \: \: \: \: \: \: \: Volume \: of \: one \: pit \: = (2000 \times 600 \times 80) {cm}^{3} }{ \: }}$

$\sf{{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⟼ \: \: \: \: \: \: \: Volume _{(pit)} = \pink{96000000 {cm}^{3}} \: }{ \: }}$

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~ Formula Used :

$\sf \pink {⇢} \: \small{\underline{{\boxed{\sf{\red{Number \: of \: planks \: that \:can \: be \: stored = \frac{Volume \: of \: one \: pit}{Volume \: of \: plank} }}}}}}$

~ Calculating the number of planks :

$\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⟼ \: \: \: \: \: \: \: Number \: of \: planks \: that \: can \: be \: stored = \: \frac{96000000}{125000} }$

$\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⟼ \: \: Number \: of \: planks \: that \: can \: be \: stored = \pink{768}}$

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~ Therefore :

The number of planks that can be stored is 768.

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Answer 2

Step-by-step explanation:

The dimensions of the plank are

Length = 5m = 500cm

Breadth = 25cm

Height = 10cm

We know that

Volume of the plank = l × b × h

By substituting the values

Volume of the plank = 500 × 25 × 10

So we get

Volume of the plank = 125000 cm3

The dimensions of the pit are

Length = 20m = 2000 cm

Breadth = 6m = 600 cm

Height = 80cm

We know that

Volume of one pit = l × b × h

By substituting the values

Volume of one pit = 2000 × 600 × 80

So we get

Volume of one pit = 96000000cm3

So the number of planks that can be stored = Volume of

one pit/ Volume of plank

By substituting the values

Number of planks that can be stored = 96000000/125000

So we get

Number of planks that can be stored = 768