Page 180 - Maths Skills - 8
P. 180

178                                                                                                  Maths

          2.  The dimensions of a cuboidal box are 2m 50 cm × 1 m 25 cm × 75 cm. Find

             (i)  the area of canvas required to cover this box; and
            (ii)  the cost of canvas for covering the box at the rate of ` 4 per square metre.
          3.  The paint in a certain container is sufficient to paint an area equal to 9375 cm . How many bricks of
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            dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?
          4.  A cuboidal metallic box is 40 cm long, 30 cm wide and 20 cm high. Find the total surface area and
            lateral surface area of the box.
          5.  Each edge of a cube is 18 cm long. Find the total surface area and the lateral surface area of the cube.

          6.  The length, breadth and height of a cuboid are in the ratio of 4 : 3 : 2, and its total surface area is 5200
            cm . Find the dimensions of the cuboid.
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          7.  The walls and ceiling of a room are to be painted. If the length, breadth and height of the room are
            respectively 5.5 m, 3 m and 4.5 m, find the area to be painted.
          8.  Find the total surface area and the lateral surface area of the following cuboids whose dimensions are.
             (i)  l = 9 cm, b = 7 cm, h = 3 cm.               (ii)  l = 13 cm, b = 5 cm, h = 7 cm.

          9.  A swimming pool is 18 m in length, 14 m in breadth and 5 m in depth. Find the cost of cementing its
            floor and walls at the rate of  ` 12 per m .
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          10. Three equal cubes of side 5 cm are placed together. Find (i) the total surface area; and (ii) the lateral
            surface area of the resulting cuboid.
          11. Find the cost of painting a cube at ` 9.50 per m  whose edge is 5 m.
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          12. The lateral surface area of a cube is 256 cm . Find its total surface area.
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          13. The total surface area of a cube is 294 m . Find its volume.
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          14. The volume of a cube is 216 m . Find its total surface area.
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          15. The floor of a rectangular hall has a perimeter of 200 m. If its height is 5 m, find the cost of painting its
            four walls at the rate of ` 25 per sq. m.

        VOLUME OF CUBOID AND CUBE
        The space occupied by a cuboid or a cube is called its volume.

        The  standard  unit  of  volume  is  1  cubic  cm  or  1 cm , i.e., the  volume occupied  by  a  cube of side 1 cm.
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        Consider a cuboid of length (l) = 5 cm, breadth (b) = 3 cm and height (h) = 2 cm.
        Divide it into small cubes, each of side 1 cm as shown in Fig.

        Clearly in Fig., there are 30 equal cubes each of 1 cm .                                                   h
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               \ The volume of the cuboid = 30 cm .
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        Also, if we multiply length, breadth and height, we get, (5 × 3 × 2) cm  = 30 cm .                       b
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               \       The volume of a cuboid = length × breadth × height.                          l

        In cube, length = breadth = height = side

               \       Volume of a cube = (side) .
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        The other units of volume are mm , dm , m , etc.
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