Question

The length and breadth of a playground are 24m by 20m .Find the cost of covering it with gravel 1.5cm deep, if the gravel costs Rs.15 per m³​

Answer 1

Answer :-

$\: \: \boxed{\boxed{\rm{\mapsto \: \: \: Firstly \: let's \: understand \: the \: concept \: used}}}$

Here the concept of Volume or Cuboid has been used. Volume is length multiplied by breadth multiplied by height. Here we are given the dimensions of of Playground. We can multiply them all to form the volume and then multiply it with rate. Let's do it !!

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★ Formula Used

$\: \\ \: \large{\boxed{\boxed{\sf{Volume \: of \: Cuboid \: = \: \bf{Length(L) \: \times \: Breadth(B) \: \times \: Height(H)}}}}}$

$\: \\ \: \large{\boxed{\boxed{\sf{Total \: cost \: of \: gravelling \: it \: = \: \bf{Rate_{(in \: per \: m^{3})} \: \times \: Volume \: of \: Playground_{(to \: be \: gravelled)}}}}}}$

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★ Question :-

The length and breadth of a playground are 24m by 20m .Find the cost of covering it with gravel 1.5cm deep, if the gravel costs Rs.15 per m³.

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★ Solution :-

Given,

» Length of the playground = L = 24 m

» Breadth of the playground = B = 20 m

» Height of the playground = H = 1.5 cm

= 0.015 m

(This is the height to which the gravel has to be raised)

» Rate of gravelling per m³ = Rs. 15

~ For Volume of the Gravel Required :

$\: \\ \qquad \: \large{\sf{\Longrightarrow \: \: \: Volume \: of \: Cuboid \: = \: \bf{Length(L) \: \times \: Breadth(B) \: \times \: Height(H)}}}$

$\: \\ \qquad \: \large{\sf{\Longrightarrow \: \: \: Volume \: of \: Cuboid \: = \: \bf{24 \: m \: \times \: 20 \: m \: \times \: 0.015 \: m \: \: = \: \: \underline{\underline{7.2\: m^{3}}}}}}$

$\: \\ \: \large{\underline{\boxed{\tt{Volume \: \: of \: \: Gravel \: \: Required_{(for \: \: gravelling \: \: playground)} \: \: = \: \: \bf{7.2\: \: m^{3}}}}}}$

~ For Cost of Gravelling the Playground :-

$\: \\ \qquad \: \large{\sf{\Longrightarrow \: \: \: Total \: cost \: of \: gravelling \: it \: = \: \bf{Rate_{(in \: per \: m^{3})} \: \times \: Volume \: of \: Playground_{(to \: be \: gravelled)}}}}$

$\: \\ \qquad \: \large{\sf{\Longrightarrow \: \: \: Total \: cost \: of \: gravelling \: it \: = \: \bf{Rs. \: 15 \: per \: m^{3} \: \: \times \: \: 7.2\: m^{3} \: \: = \: \: \underline{\underline{Rs. \: 108}}}}}$

$\: \\ \: \large{\underline{\boxed{\tt{Cost \: \: of \: \: Gravelling \: \: the \: \: playground \: \: = \: \: \bf{Rs.\: \: 108}}}}}$

$\: \\ \large{\underline{\underline{\rm{Thus \: total \: cost \: of \: gravelling \: the \: field \: \: is \: \: \boxed{\bf{Rs. \: 108}}}}}}$

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$\: \\ \: \large{\underline{\sf{\leadsto \: \: Confused? \: Don't \: worry \: let's \: verify \: it \: :-}}}$

For verification, we need to simply apply the values we got into the equation formed.

We know that rectangles formes along z axis forms Cuboid. Then,

=> Area of playground × Height = Volume

=> 20 × 24 × 0.015 = 7.2

=> 7.2 m³ = 7.2

Clearly, LHS = RHS

So our answer is correct.

Hence, Verified.

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$\: \: \large{\underline{\underline{\rm{More \: to \: know \: :-}}}}$

• Volume of Cube = (Side)³

• Volume of Cylinder = πr²h

• Volume of Cone = ⅓ × πr²h

• Volume of Hemisphere = ⅔ × πr³

Answer 2

Given,

The length and breadth of a playground are 24m by 20m and gravel costs Rs.15 per m³​

To find :

Find the cost of covering it with gravel 1.5cm deep.

Solution :

Given, length and breadth of playground = 24m by 20 m

Now, depth of gravel = 1.5 cm = (1.5/100) m = 0.015 m

Now volume of playground = l * b * h

⇒  Volume of playground = 24 * 20 * 0.015

⇒  Volume of playground = 7.2 m³

Now cost of covering with gravel :

⇒ Cost of covering = 7.2 * 15

⇒ Cost of covering = 108

⇒ Cost of covering = Rs. 108

Therefore,

Cost of covering with gravel = Rs. 108