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Mensuration

Long Answer Type

81. The area of a rhombus and that of a square are equal. The side of the square is 6 cm. If one of the diagonal of the rhombus is 4 cm, then find the length of its other diagonal.

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Short Answer Type

82. If the length, breadth and height of a cuboid are respectively equal to 6 cm, 4 cm and 7 cm, then find its total surface area.

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Long Answer Type

83. The edge of a cube is 2 cm. Find the total surface area of the cuboid formed by three such cubes joined edge to edge.

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Short Answer Type

84. A company is selling its suitcases according to their surface areas. A suitcase can be bought at the rate of Rs 0.05 per cm². If the size of the suitcase purchased by Ramita is 80 cm × 48 cm × 24 cm, find the cost paid by Ramita for such 100 suitcases.

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85. A closed cylindrical tank of radius 7 cm and height 5 m is made from a sheet of metal. If the breadth of the rectangular sheet is 10 m, then find the length of the sheet.

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Long Answer Type

86. A road roller makes 250 complete revolution to move once over to once level a road. Find the area of the road levelled if the diameter of the road roller is 84 cm and length is 1 m.

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Short Answer Type

87. A cuboid is of dimensions 50 cm × 45 cm × 30 cm. How many small cubes with sides 5 cm can be places in the given cuboid?

Volume of a cuboid = Length x Breadth x Height
Here, Length of the cuboid = 50 cm
Breadth of the cuboid = 45 cm
Height of the cuboid = 30 cm
∴ Volume of the cuboid = 50 x 45 x 30 cm³
Volume of the small cube = Side x Side x Side
= 5 x 5 x 5 cm³ Let the number of the required small cubes = x
∴ x x (5 x 5 x 5) = 50 x 45 x 30
$rightwards double arrow$ $straight x equals fraction numerator 50 cross times 45 cross times 30 over denominator 5 cross times 5 cross times 5 end fraction$
= 10 x 9 x 6
= 540
Thus, 540 smalles cubes can be placed in the given cuboid.

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88. A square and a rectangle have same perimeter. If the side of the square is 60 cm and length of the rectangle is 80 m, then whose area is more and how much?

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89. Find the perimeter of a semicircular figure, if its diameter is 2.8 cm.

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90. Find the area of the trapezium shown below.

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