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Surface Areas and Volumes

Short Answer Type

11. A closed iron tank 12 m long, 9 m wide and 4 m deep is to be made. Determine the cost of iron sheet used at the rate of र 50 per metre, the sheet being 2 m wide.

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12. A table cover 4 m x 2 m is spread on a table. Find the cost of polishing the top of the table at र40 per square metre of 25 cm table cover is hanging all round the table.

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13. The cost of papering the four walls of a room at 70 paise per square metre is र 157.50. The height of the room is 5 metres. Find the length and the breadth of the room if they are in the ratio 4 : 1.

Let the length and the breadth of the room be 4x m and x m respectively.
Area of the four walls of the room = 2(l + b) h
= 2(4x + x) 5 = 50 x m²Cost of papering the four walls of the room @ 70 paise per square metre
= र 50x x 0.70 = र 35x According to the question,
35x = 157.50

$rightwards double arrow space space space space space space space space space space straight x equals space fraction numerator 157.50 over denominator 35 end fraction equals 4.5$

∴ Breadth of the room = 4.5 m
∴ Length of the room = 4 x 4.5 m = 18 m.

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14. A classroom is 7 m long, 6.5 m wide and 4 m high. It has one door 3 m x 1.4 m and three windows each measuring 2 m x 1 m. The interior wall is to be colour washed. Find the cost of colour washing at the rate of र 3.50 per m².

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15. Two cubes of side 6 cm each, are joined end to end. Find the surface area of the resulting cuboid.

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16. The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost of covering it with sheet of paper at the rates of र 8 and र 9.50 per m² is र1248. Find the dimensions of the box.

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17. The length, breadth and height of a cuboid are 15 cm, 10 cm and 20 cm. Find the surface area of the cuboid.

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18. Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden block covered with coloured paper with picture of Santa Claus on it (see figure). She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth and height as 80 cm, 40 cm and 20 cm respectively how many square sheets of paper of side 40 cm would she require?

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19. Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm (see figure). Find how much he would spend for the tiles, if the cost of the tiles is र 360 per dozen.

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20. Three cubes each of the side 3 cm are joined end to end. Find the surface area of the resulting cuboid.

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