Question

The area of a square pond is 5625 m² and a 2 m wide path is made around the pond.

(i) Find the area of the path

(ii) Calculate the number of tile each of 40 cm x 20 cm required to pave the path.

(iii) If the cost of a tile is Rs 35, find the cost of paving the path.​

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

→ Area of square = 5625m²

→ (side)² = 5625m²

→ (side)² = (75)²

→ side of Square = 75m.

Now a 2m wide path is made around the Pond.

So,

→ Area of Path = Area of outer Square - 5625

→ Area of Path = (75 + 2*2)² - 5625

→ Area of Path = (79)² - 5625

→ Area of Path = 6241 - 5625

→ Area of Path = 616m² (Ans.)

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Now,

→ The number of tiles required to pave the path = (Area of Path) / (Area of Each Tile).

→ Tiles Required = 6160000/(20*40) {1m² = (100 * 100)cm²}

→ Tiles Required = 7700 Tiles. (Ans.)

_____________________

And,

=> cost of a Tile = Rs.35

=> cost of 7700 Tiles = Rs.269500 (Ans.)

Hence, cost of paving the path. is Rs.269500.

____________________________

Answer 2

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

• Area of square pond = 5625 m²
• 2 m wide path is made around the pond.

${\bf{\blue{\underline{Now:}}}}$

$\star {\sf{Area \: of \: each \: square \: pond = side \times side}}$

$: \implies{\sf{ 75 \times 75{m}^{2} }}$

It is given that the 2m wide path is made around the pond.

${\sf{(1). area \: of \: path = (75 + 2 \times 2 ) ^{2} - 5625 }}$

$: \implies{\sf{ (75 + 4) ^{2} - 5625}}$

$: \implies{\sf{ (79) ^{2} - 5625}}$

$: \implies{\sf{ 6241 - 5625}}$

$: \implies{\sf{616{m}^{2}}}$

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$\star {\sf{so \: the \: number \: of \: tiles \: required = \frac{surface \: area \: of \: the \: path}{area \: of \: tile \: } }}$

$: \implies{\sf{ \: \frac{616 {m}^{2} }{40 \times 20cm} }}$

$: \implies{\sf{ \: \frac{616 \times 10000c {m}^{2} }{40 \times 20c {m}^{2} } }}$

$: \implies{\sf{ \: \frac{616 0000c {m}^{2} }{800c {m}^{2} } }}$

$: \implies{\sf{ 7700 }}$

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$\star {\sf{ cost \: of \: the \: tile \: = 30 \: rs}}$

$\star{\sf{ cost \: of \: 7700 \: tile \: = 30\times7700}}$

$: \implies{\sf{269500 \: rs }}$

___________________________________

Hence,

• the area of the path = 616m²
• Required tiles = 7700
• Cost of paving path = 269500Rs