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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.

Here, Radius (r) = 7 cm
Height (h) = 5 cm
Since, total surface area of the closed cylinder
$space space equals 2 πr left parenthesis straight r plus straight h right parenthesis$
∴ Total surface area of the cylinder tank
$equals space 2 cross times 22 over 7 cross times left parenthesis 7 right parenthesis cross times left parenthesis 7 plus 5 right parenthesis space straight m squared$
$equals space 2 cross times 22 cross times 12 space straight m squared$
$equals space 528 space straight m squared$
Let, the length of the sheet required = 'l' m
∴ Area of the rectangular sheet = l x 10 m²
$rightwards double arrow$ l x 10 = 528
$rightwards double arrow$ $straight l equals 528 over 10 space straight m$

= 52.8 m
Thus, the required length of the sheet = 52.8 m.

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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?

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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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