Question

The length of a room is double of its breadth and 5 times
of its height. If volume of the room is 800 m³, find the cost
of plastering its 4 walls at Rs. 18 per m2. (Ans: Rs. 4320)​

Answer 1

Answer:

Let Length Of The Room Be Taken as x

Now,

Length ( l ) = x cm

Breadth ( b ) = x / 2 cm

Height ( h ) = x / 5 cm

Volume of the Room = Length x Breadth x Height

800 = (x) x (x / 2) x (x / 5)

800 x 5 x 2 = x^3

x^3 = 8000

x = 20 cm

Therefore,

Length = x = 20 cm

Breadth = x / 2 = 20 / 2 = 10 cm

Height = x / 5 = 20 / 5 = 4 cm

Area of Four Walls = 2 x ( Length + Breadth ) x Height

                             = 2 x ( 20 + 10 ) x 4

                             = 240 m ^2

Now,

Cost of Plastering at Rate Rs.18/m^2 = 240 x 18

                                                        = Rs. 4320

Answer 2

Answer:

Rs. 4320

Step-by-step explanation:

$\tt\color{blue} {given : }$

• Length of the room is double of its breadth = X
• Breath and 5 times of its height.
• Volume of the room = 800m³

$\tt\color{blue} {to \: find : }$

• To find the cost of plastering its 4 walls

$\tt\color{blue} {solution : }$

Let length of room be X

According to question,

$\tt Length \: of \: room = 2× breath \: of \: room$

$\tt : ⟹ \frac{1}{2} (length \: of \: room) = breath \: of \: room$

$\tt : ⟹ \frac{1}{2} x = breath \: of \: room$

$\tt: ⟹breath \: of \: room \: = \frac{x}{2}$

$\color {red} \tt according \: to \: questions \:$

$\tt \: length \: of \: room \: = 5 \: height \: of \: room$

$\tt :⟹ \frac{1}{5} (length \: of \: room \: ) = height \: of \:room$

$\tt : ⟹ \frac{1}{5} x = height \: of \: room$

$\tt: ⟹height \: of \: room \: = \frac{1}{5} x$

$\color{purple} \tt \: now$

$\tt \: length \: = x \\ \\ \tt \: breath \: = \frac{x}{2} \\ \\ \tt \: height \: = \frac{x}{5}$

According to question,

• Volume of the room = 800m³

$\tt \: length \: \times breath \: \times height \: = 800$

$\tt: ⟹(x) \times \bigg( \frac{x}{2} \bigg) \times \bigg ( \frac{x}{5} \bigg ) = 80$

$\tt: ⟹ {x}^{3} = 800 \times 10$

$\tt: ⟹ {(x)}^{3} = {(20 \times 20 \times 20)}^{3}$

$\tt \boxed{ : ⟹x = 20}$

$\color{green} \tt \: length \: = x \tt = 20$

$\tt \color{green} breath \: = \frac{x}{2} \tt = \frac{10}{2} = 10cm$

$\tt \color{green}height \: = \frac{x}{5} = \frac{20}{5} = 4cm$

$\tt \: Area \: of \: four \: walls = 2(length + breath)height \:$

$\tt: ⟹2(20 + 10) \times 4$

$\tt: ⟹2 \times (30 \times 4)$

$\tt: ⟹240 {m}^{3}$

$\tt \: Cost \: of \: plastering \: its \: walls = 18 \: per/m³$

$\tt \: Total \: cost \: of \: plastering \: its \: 4 \: walls = 240 \times 18$

$\huge\color{green} \boxed{ \tt =4320 }$