Question

Dimensions of a swimming pool are 5 m by 4 m by 3 m. The cost of cementing its four walls and floor at the rate of Rs 100 per square meter will be​

Answer 1

◘ Given ◘

Dimensions of a swimming pool are 5 m by 4 m by 3 m.

Let us take :

• Length, l = 5 m
• Breadth, b = 4 m
• Height, h = 3 m

◘ To Find ◘

The cost of cementing its four walls and floor at the rate of Rs 100 per square meter.

◘ Solution ◘

The required area of the swimming pool = LSA + base area

→ A = 2h (l + b) + lb

→ A = 2 × 3(5 + 4) + (5 × 4)

→ A = 6(9) + 20

→ A = 54 + 20

→ A = 74 m²

_________________

As it costs Rs 100 per square meter,

The total cost of cementing its four walls and floor = 100 × 74

→ Total cost = ₹ 7400

Therefore, the total cost of cementing its four walls and floor at the rate of Rs 100 per square meter will be Rs 7400.

Answer 2

Answer :

$\dag\:\boxed{\bf\underline{Cost\:of\:Cementing\:Four\:walls\:and\:the\:Floor\:is\:7400\:Rs\:\: .}}\:\dag$

Explanation :

Given :–

• Dimensions of the Swimming pool are 5 m × 4 m × 3 m .
• Cost of Cementing per square meter is 100 Rs.

To Find :–

• Cost of cementing four walls and the floor of the Swimming Pool .

Formula Applied :–

• $\boxed{\bf{\star\:\:Total\:Surface\:Area\:of\:Cuboid\:=\:2(lb\:+\:bh\:+\:hl)\:\:\star}}$

• $\boxed{\bf{\star\:\:Area\:of\:Rectangle\:=\:l\:\times\:b\:\:\star}}$

Solution :–

We have Length(l) = 5 m , Breadth(b) = 4 m and Height(h) = 3 m .

Putting these values in the Total Surface Area of Cuboid formula :

$\rightarrow\sf{Total\:Surface\:Area\:of\:Pool\:=\:2[(5\:\times\:4)\:+\:(4\:\times\:3)\:+\:(3\:\times\:5)]}$

$\rightarrow\sf{Total\:Surface\:Area\:of\:Pool\:=\:2(20\:+\:12\:+\:15)}$

$\rightarrow\sf{Total\:Surface\:Area\:of\:Pool\:=\:(2\:\times\:47) \:m^2}$

$\rightarrow\boxed{\sf{Total\:Surface\:Area\:of\:Pool\:=\:94 \:m^2}}$

Now , we will find the area of Rectangular Top :-

$\rightarrow\sf{Area\:of\:Rectangular\:Top\:of\:the\:Pool\:=\:(5\:\times\:4)\:m^2}$

$\rightarrow\boxed{\sf{Area\:of\:Rectangular\:Top\:of\:the\:Pool\:=\:20\:m^2}}$

So now we will find the area of four walls and the floor :-

According to the given Condition :

Area of Four walls and the Floor = T.S.A. of Pool - Rectangular Top Area

$\rightarrow\sf{Area\:of\:Four\:walls\:and\:the\:Floor\:=\:(94\:-\:20)\:m^2}$

$\rightarrow\boxed{\bf{Area\:of\:Four\:walls\:and\:the\:Floor\:=\:74\:m^2}}$

∴ The Cost of Cementing will be =  74 × 100 Rs. = 7400 Rs.