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Let the dimensions of the box be 2k, 3k and 4k. Total surface area = 2(lb + bh + hl) = 2(2k ⋅ 3k + 3k ⋅ 4k + 4k ⋅ 2k) = 52k 2 m 2 Cost of covering at the rate of र 8 per m 2 = 52k 2 x 8 = र416 k 2 Cost of covering at the rate of र 9.50 per m 2 = 52k 2 x 9.50 = र 494k 2 Difference between the costs = र 494k 2 – र 416k 2 = र 78k 2 According to the question, 78k 2 = 1248 ⇒ k 2 = 16 ⇒ k = 4 Hence, the dimensions of the box are 8 m, 12 m and 16 m.

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Surface Areas and Volumes

Short Answer Type

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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.

Let the dimensions of the box be 2k, 3k and 4k.
Total surface area = 2(lb + bh + hl)
= 2(2k ⋅ 3k + 3k ⋅ 4k + 4k ⋅ 2k)
= 52k² m²Cost of covering at the rate of र 8 per m² = 52k² x 8 = र416 k²Cost of covering at the rate of र 9.50 per m² = 52k² x 9.50 = र 494k²Difference between the costs = र 494k² – र 416k² = र 78k²According to the question,
78k² = 1248 ⇒ k²= 16 ⇒ k = 4 Hence, the dimensions of the box are 8 m, 12 m and 16 m.

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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.