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Volume and Surface Area of Solid Figures

  1. The volume of a cube is 512 cm3, Its surface area is ?
    1. 64 cm2
    2. 256 cm2
    3. 384 cm2
    4. 512 cm2
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    ∵ a3 = 512 = 8 x 8 x 8
    ⇒ a = 8 cm
    ∵ Surface area = 6a2

    Correct Option: C

    ∵ a3 = 512 = 8 x 8 x 8
    ⇒ a = 8 cm
    ∵ Surface area = 6a2
    =[6 x (8)2] cm2
    =384 cm2

    Report

  1. The surface area of a cube is 726 m2. Its volume is ?
    1. 1300 m3
    2. 1331 m3
    3. 1452 m3
    4. 1542 m3
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    Surface area = 6a2 = 726

    Correct Option: B

    Surface area = 6a2 = 726
    ⇒ a2 = 121
    ⇒ a = 11 cm
    ∴ Volume of the cube = (11 x 11 x 11) cm3
    = 1331 cm3

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  1. If each side of a cube is doubled, then its volume? .
    1. Is doubled
    2. Becomes 4 times
    3. Becomes 6 times
    4. Becomes 8 times
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    Let the edge of original cube = x cm
    Edge of new cube = (2x) cm
    Ratio of their volumes = x3 : (2x)3

    Correct Option: D

    Let the edge of original cube = x cm
    Edge of new cube = (2x) cm
    Ratio of their volumes = x3 : (2x)3
    = x3 : 8x3
    = 1 :8

    Thus the volumes be comes 8 times.

    Report

  1. Three metal cubes of sides 5 cm, 4 cm and 3 cm are melted and recast into a new cube. The length of the edge of this cube, is ?
    1. 6 cm
    2. 8 cm
    3. 10 cm
    4. None of these
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    Volume of new cube = (5)3 + (4)3 + (3)3 cm3

    Correct Option: A

    Volume of new cube = (5)3 + (4)3 + (3)3 cm3
    = 126 cm3

    Edge of this cube = (6 x 6 x 6)1/3 = 6 cm

    Report

  1. If the volumes of two cubes are in the ratio 8 : 1, the ratio of their edges, is ?
    1. 8 : 1
    2. 2√2 : 1
    3. 2 : 1
    4. None of these
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    Volume of new cube = [(5)3 + (4)3 + (3)3] cm3

    Correct Option: A

    Volume of new cube = [(5)3 + (4)3 + (3)3] cm3
    = 216 cm3
    Edge of this cube = ( 6 x 6 x 6)1/3 = 6 cm

    Report

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