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. [Hint : Area of the four walls = Lateral surface area.]

Let the length, breadth and height of the rectangular hall be l m, b m and h m respectively.

Perimeter = 250 m

⇒ 2(l + b) = 250

⇒ l + b = 125 ...(1)

Area of the four walls

Hence, the height of the hall is 6 m.

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A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.

(i) Which box has the greater lateral surface area and by how much?

Each edge of the cubical box (a) = 10 cm

∴ Lateral surface area of the cubical box = 4a^{2} = 4(10)^{2} = 400 cm^{2}.

For cuboidal box

l = 12.5 cm b = 10 cm h = 8 cm

Lateral surface area of the cuboidal box = 2(l + b) h

= 2(12.5+ 10)(8) = 360 cm^{2}.

∴ Cubical box has the greater lateral surface area than the cuboidal box by (400 – 360) cm^{2}, i.e., 40 cm^{2}.

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(i) The area of the sheet required for making the box.

(ii) The cost of sheet for it, if a sheet measuring 1 m^{2} costsर 20.

(i) l = 1.5 m

b= 1.25 m

h = 65 cm = 0.65 m.

∴ The area of the sheet required for making the box = lb + 2(bh + hl)

= (1.5)(1.25) + 2 {(1.25)(0.65) + (0.65)(1.5)} = 1.875 + 2{0.8125 + 0.975}

= 1.875 + 2(1.7875) = 1.875 + 3.575 = 5.45 m^{2}.

(ii) The cost of sheet for it = र 5.45 x 20 = र 109.

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The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of र 7.50 per m^{2}.

l = 5 m

b = 4 m

h = 3 m

Area of the walls of the room = 2(l + b) h

= 2(5 + 4) 3 = 54 m^{2}Area of the ceiling = lb

= (5) (4) = 20 m^{2}∴ Total area of the walls of the room and the ceiling = 54 m^{2} + 20 m^{2} = 74 m^{2}∴ Cost of white washing the walls of the room and the ceiling = 74 x 7.50 = र 555.

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The paint in a certain container is sufficient to paint an area equal to 9.375 m2. How many bricks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?

For a brick

l = 22.5 cm b = 10 cm h = 7.5 cm

∴ Total surface area of a brick = 2 (lb + bh + hl)

= 2(22.5 x 10 + 10 x 7.5 + 7.5 x 22.5)

= 2(225 + 75 + 168.75)

= 2(468.75) = 937.5 cm^{2} = .09375 m^{2}∴ Number of bricks that can be painted out

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