Question

The perimeter of the Hoor of a hall is 300 m and its height is 6 m. Find the cost of the painting the four walls at the rate of R 15 per square metre.​

Answer 1

Given : Perimeter of the hall is 300 m and its height is 6 m . Rate of painting is Rs.15 per m² .

To Find : Find the Cost of Painting the wall

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SolutioN :

$\maltese$ Formula Used :

$\qquad \; {\orange{\bigstar \; \; {\pink{\underbrace{\underline{\green{\sf{ Perimeter{\small_{(Rectangle)}} = 2 \bigg( Length + Breadth \bigg) }}}}}}}}$

$\qquad \; {\orange{\bigstar \; \; {\pink{\underbrace{\underline{\green{\sf{ LSA{\small_{(Cuboid)}} = 2 \bigg( Length + Breadth \bigg) \times Height }}}}}}}}$

$\maltese$ Calculating the Value of L + B :

$\begin{gathered} \qquad \; \implies \; \; \sf { Perimeter = 2 \bigg( Length + Breadth \bigg) } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \implies \; \; \sf { 300 = 2 \bigg( Length + Breadth \bigg) } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \implies \; \; \sf { \dfrac{300}{2} = Length + Breadth } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \implies \; \; \sf { \cancel\dfrac{300}{2} = Length + Breadth } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \implies \; \; {\underline{\boxed{\pmb{\sf{ Length + Breadth = 150 \; m }}}}} \; {\pink{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\maltese$ Calculating the Cost of Painting :

$\begin{gathered} \dashrightarrow \; \; \sf { Cost = LSA \times Rate } \\ \\ \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { Cost = 2 \bigg\{ \bigg( L + B \bigg) \times h \bigg\} \times Rate } \\ \\ \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { Cost = 2 \bigg( 150 \times 6 \bigg) \times 15 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { Cost = 2 \times 900 \times 15 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { Cost = 1800 \times 15 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; {\underline{\boxed{\pmb{\sf{ Cost = Rs. \; 27000 }}}}} \; {\purple{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\therefore \;$ Cost of Painting the four walls is Rs.27000 .

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:)

Answer 2

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Given: The perimeter of the floor of the rectangular hall is 250m and the cost of painting the four walls at the rate of ₹10 per m² is ₹15000.

The area of the four walls of the cuboidal room will be the Lateral surface area of the cuboid.

Lateral surface area of cuboid = 2(l + b)h

The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ₹10 per m2 is ₹15000, find the height of the hall.

The area of the four walls can also be obtained by dividing the total cost of the painting by the rate of painting per m2.

Let the length, breadth, and height of the room be l, b, and h respectively. The cost of painting the four walls is ₹15000.

The rate of painting is ₹10 / m2

Perimeter of the floor = 250 m

Therefore, 2(l + b) = 250 m ------------ (1) [Since, perimeter of a rectangle = 2(l + b)

Now, Area of four walls = 15000/10 m2 = 1500 m2

2(l + b)h = 1500 m2 [From equation(1)]

250 m × h = 1500 m2

h = 1500 m2/250 m = 6 m

Thus, the height of the hall is 6 m.