Question

Ramesh has build a cuboidal water tank with lid for his house with each outer edges 1.5 cm long. He gets the outer surface of tank by excluding the base , covered with square tiles of side 25 cm . find how much he spend on tiles, if cost of tiles ₹ 400 per dozen .​

Answer 1

$\large{\underline{\rm{\purple{\bf{Given:-}}}}}$

Length of the outer edge = 1.5 cm

Length of the side of each square = 25 cm

Cost per dozen tiles = Rs. 400

$\large{\underline{\rm{\purple{\bf{To \: Find:-}}}}}$

Number of tiles required.

The cost of the tiles.

$\large{\underline{\rm{\purple{\bf{Solution:-}}}}}$

$\sf Number \: of \: tiles \: required=\dfrac{Surface \: area \: of \: tiles}{Area \: of \: each \: tile}$

We put tiles on 5 faces, one face is of form square

$\underline{\red{\boxed{\sf Area \: of \: a \: square = Side \times Side}}}$

Area of 5 faces = 5 × Area of 1 face

$\implies \sf 5 \times Side^{2}$

Substitute their values,

$\implies \sf 5 \times (1.5)^{2}$

$\implies \sf 5 \times (1.5 \times 100)^{2}$

$\implies \sf 5 \times (150)^{2} \: cm^{2}$

Now, finding the area of tile,

The tile is in the form of square with each side 25 cm

Area of 1 tile = Side × Side

Area of 1 tile = 25 × 25 cm²

$\sf Number \: of \: tiles \: required =\dfrac{Area \: of \: 5 \: faces}{Area \: of \: 1 \: tile}$

Substituting their values,

Number of tiles required = $\sf \dfrac{5 \times (150)^{2}}{25 \times 25}$

$\implies \sf \dfrac{5 \times 150 \times 150}{25 \times 25}$

$\implies \sf 180 \: tiles$

Next, finding the cost of tiles

Given that, 1 dozen of tiles costs Rs. 400

1 dozen = 12

So, 12 tiles costs Rs. 400

Cost of 1 tile = $\sf \dfrac{Cost \: of \: one \: dozen}{12}$

Cost of 1 tile = $\sf \dfrac{400}{12}$

∴ Cost of 180 tiles = $\sf Rs. \: \dfrac{400}{12} \times 180$

Cost of 180 tile = Rs. 6000

Therefore, the cost of 180 tiles is Rs. 6000

Answer 2

Given:−

Length of the outer edge = 1.5 cm

Length of the side of each square = 25 cm

Cost per dozen tiles = Rs. 400

\large{\underline{\rm{\purple{\bf{To \: Find:-}}}}}ToFind:−

Number of tiles required.

The cost of the tiles.

\large{\underline{\rm{\purple{\bf{Solution:-}}}}}Solution:−

\sf Number \: of \: tiles \: required=\dfrac{Surface \: area \: of \: tiles}{Area \: of \: each \: tile}Numberoftilesrequired=AreaofeachtileSurfaceareaoftiles

We put tiles on 5 faces, one face is of form square

\underline{\red{\boxed{\sf Area \: of \: a \: square = Side \times Side}}}Areaofasquare=Side×Side

Area of 5 faces = 5 × Area of 1 face

\implies \sf 5 \times Side^{2}⟹5×Side2

Substitute their values,

\implies \sf 5 \times (1.5)^{2}⟹5×(1.5)2

\implies \sf 5 \times (1.5 \times 100)^{2}⟹5×(1.5×100)2

\implies \sf 5 \times (150)^{2} \: cm^{2}⟹5×(150)2cm2

Now, finding the area of tile,

The tile is in the form of square with each side 25 cm

Area of 1 tile = Side × Side

Area of 1 tile = 25 × 25 cm²

\sf Number \: of \: tiles \: required =\dfrac{Area \: of \: 5 \: faces}{Area \: of \: 1 \: tile}Numberoftilesrequired=Areaof1tileAreaof5faces

Substituting their values,

Number of tiles required = \sf \dfrac{5 \times (150)^{2}}{25 \times 25}25×255×(150)2

\implies \sf \dfrac{5 \times 150 \times 150}{25 \times 25}⟹25×255×150×150

\implies \sf 180 \: tiles⟹180tiles

Next, finding the cost of tiles

Given that, 1 dozen of tiles costs Rs. 400

1 dozen = 12

So, 12 tiles costs Rs. 400

Cost of 1 tile = \sf \dfrac{Cost \: of \: one \: dozen}{12}12Costofonedozen

Cost of 1 tile = \sf \dfrac{400}{12}12400

∴ Cost of 180 tiles = \sf Rs. \: \dfrac{400}{12} \times 180Rs.12400×180

Cost of 180 tile = Rs. 6000

Therefore, the cost of 180 tiles is Rs. 6000