Question

Swimming pool is 20 m in length 15 m in breadth 4 m in depth find the cost of cementing the floor and walls of rupees 35 per metre

Answer 1

₹ 20,300

The question states that a swimming pool is 20 m in length, 15 m in Breadth and 4 m in depth. & we're asked to calculate the cost of cementing the floor and walls at ₹ 35 per metre. So, Cement has to be done on four sides and the bottom. Therefore,

• Length = 20 m

• Breadth = 15 m

• Height = 4 m

• Rate = ₹ 35 per m

⠀

$\twoheadrightarrow\sf\quad Area_{\:(cemented)} = TSA - Area_{\;(top)}$

$\twoheadrightarrow\sf\quad 2\Big\{L \times B \Big\} + \Big\{B \times H \Big\} + \Big\{H \times L\Big\} - \Big\{L \times B\Big\}$

$\twoheadrightarrow\sf\quad 2\Big\{20 \times 15\Big\} + \Big\{15\times4\Big\} + \Big\{4 \times 20\Big\} - \Big\{20 \times 15\Big\}$

$\twoheadrightarrow\sf\quad 2\Big\{300 + 60 + 80\Big\} - 300$

$\twoheadrightarrow\sf\quad 2 \times 440 - 300$

$\twoheadrightarrow\sf\quad 880 - 300$

$\twoheadrightarrow\quad\underline{\boxed{\pmb{\frak{580\;m^2}}}}\;\bigstar$

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• C o s t⠀o f⠀c e m e n t I n G :

★ Cost = (Given rate × Area of the Pool) ★

↠⠀Cost = 35 × 580

↠⠀Cost = ₹ 20,300

$\therefore$ Hence, the cost of cementing will be 20,300₹.

Answer 2

G I V E N :

Swimming pool is 20 m is length 15 m is breadth 4 m in depth find the cost of cementing the floor and walls of rupees 35 per square metre

S O L U T I O N :

GivEn Data ⤵

Length of the swimming pool = 20 m

Breadth of the swimming pool = 15 m

Height of the swimming pool = 4 m

Cost of cementing the floor and walls per sq. metre = ₹ 35

Calculation Begins ⤵

As we have been given swimming pool it should be open on the top most side and will be enclosed by all the three sides with the floor

So, here we will apply the formula for Lateral Surface Area added with the area of the floor

As we know that a swimming pool is always a rectangle

⟼ Surface area of the pool = Lateral Surface Area + Area of the floor

❒ Lateral Surface Area of Cuboid is 2(l + b)h

⟼ Surface area of the pool = 2(l + b)h + lb

⟼ Surface area of the pool = 2(20 + 15)4 + 20(15)

⟼ Surface area of the pool = 8(35) + 300

⟼ Surface area of the pool = 280 + 300

⟼ Surface area of the pool = 580 m²

Hence, the surface area is 580 m²

Finding Cost ⤵

◉ Cost of Cementing 1 m² is ₹ 35

◉ Hence, for 580 m² = ₹ 35 × 580

◉ Cost = ₹ 20300

• Cost of cementing the floor and walls is ₹ 20300

E X T R A S :

❒ For Cuboid

Total Surface Area = 2(lb + bh + hl)

Lateral Surface Area = 2h(l + b)

❒ For Cube

Total Surface Area = 6(side)²

Lateral Surface Area = 4(side)²

❒ For Cylinder

Total Surface Area = 2πr(h + r)

Lateral Surface Area = 2πrh

Here,

r refers to radius

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