Area & Volume

  1. Question: Three cubes of iron whose edges are `6`cm, `8 cm` and `10` cm respectively are melted and formed into a single cube. The edge of the new cube formed is :

    A
    `12 cm`

    B
    `14 cm`

    C
    `16 cm`

    D
    `18 cm`

    Note: Volume of new cube `= [6^3 + 8^3 + (10)^3] cu. cm` `= 1728 cu. cm`. Let the edge of new cube be a cm. Then,` a^3 = 1728` `= (4 xx 4 xx 4 xx 3 xx 3 xx 3)` `or a = 12 cm`.
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  2. Question: The surface area of a cube is `1734` sq. cms. Its volume is :

    A
    `2197 cu. cm`

    B
    `4913 cu. cm`

    C
    `2744 cu. cm`

    D
    `4096 cu. cm`

    Note: `6a^2 = 1734 ⇒ a^2 = 289` `or a = 17 cm`. :. Volume`= (17 xx 17 xx 17) cu. cm` `= 4913 cu. cm`.
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  3. Question: The surface area of a cube is `600 cm^2`. The length of its diagonal is :

    A
    `10/√3 cm`

    B
    `10/√2 cm`

    C
    `10√3 cm`

    D
    `10√2 cm`

    Note: `6a^2 = 600 ⇒ a^2 = 100` `or a = 10 cm`. `:. Diagonal = √3 a = 10√3 cm`.
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  4. Question: The volume of a cube is `2744 cu. cm.` Its surface area is :

    A
    `196 cm^2`

    B
    `1176 cm^2`

    C
    `784 cm^2`

    D
    `588 cm^2`

    Note: `a^3 = 2744` `= (2 xx 2 xx 2 xx 7 xx 7 xx 7) ⇒ a` `= 14 cm.` :. Surface Area `= 6a^2 = (6 xx 14 xx 14) cm^2` `= 1176 cm^2`.
    1. Report

  5. Question: The sum of the length, breadth and depth of a cuboid is `19` cm and its diagonal is `5√5 cm`. Its surface area is :

    A
    `361 cm^2`

    B
    `125 cm^2`

    C
    `236 cm^2`

    D
    `486 cm^2`

    Note: `(1 + b + h) ` `= 19 & √1^2 + b^2 + h^2` `= 5√5 and so (1^2 + b^2 + h^2)` `= 125` Now`(1 + b + h)^2 = 19^2` `⇒ (1^2 + b^2 + h^2) + 2 (1b + bh + 1h) = 361` `⇒ 2 (1b + bh + 1h)` `= (361 - 125)` `= 236`. :. Surface area `= 236 cm^2.`
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  6. Question: The area of the base of a rectangular tank is `6500 cm^2` and the volume of water contained in its `2.6` cubic metres. The depth of water in the tank is :

    A
    `3.5 m`

    B
    `4 m`

    C
    `5 m`

    D
    `6 m`

    Note: Volume`= (2.6 xx 100 xx 100 xx 100) cubic cm`. Depth` = Volume/Area of the base` `= ((2.6 xx 100 xx 100 xx 100)/(6500)) cm` `= 4 m`.
    1. Report

  7. Question: Given that `1` cu. cm of marble weighs `25` gms, the weight of a marble block `28` cm in width and`5` cm thick is `112` kg. The length of the block is :

    A
    `36 cm`

    B
    `40 cm`

    C
    `32 cm`

    D
    `26.5 cm`

    Note: Let length = x cm. Then` x xx 28 xx 5 xx 25/1000` `= 112` `:. x = (112 xx 1000/25 xx 1/28 xx 1/5) cm` `= 32 cm.` `:. Length of block = 32 cm`.
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  8. Question: The volume of a wall,`5` times as high as it is broad and `8` times as long as it is high, is `12.8` cu. mertres. The breadth of the wall is :

    A
    `30 m`

    B
    `40 m`

    C
    `22.5 m`

    D
    `25 m`

    Note: Let, breadth = x mertres. Then, Heigth` = 5x` mertres and length `= 40 x` mertres. `:. x xx 5x xx 40x` `= 12.8` `or x^3 = 12.8/200` `= 128/2000` `= 64/1000.` `:. x 4/10 m` `= (4/10 xx 100) cm` `= 40 cm.`
    1. Report

  9. Question: Half cubic metre of goldsheet is extended by hammering so as to cover an area of `1` hectare. The thickness of the sheet is :

    A
    `0.5 cm`

    B
    `0.05 cm`

    C
    `0.005 cm`

    D
    `.0005 cm`

    Note: Volume of gold `= (1/2 xx 100 xx 100 xx 100) cu. cm`. Area of sheet `= 10000 sq. m` `= (10000 xx 100 xx 100) sq. cm.` :. Thickness of the sheet `= ((1 xx 100 xx 100 xx 100)/(2 xx 10000 xx 100 xx 100)) cm.` `= 0.005 cm.`
    1. Report

  10. Question: In a shower, `5` cm of rain falls. The valume of water that on `1.5` hectares of ground is :

    A
    `75 cu. m`

    B
    `750 cu. m`

    C
    `7500 cu. m`

    D
    `75000 cu. m`

    Note: Area `= (1.5 xx 10000) sq. metres` `= 15000 sq. metres.` Depth`= 5/100 m = 1/20 m.` :. Volume` = (Area xx depth)` `= (15000 xx 1/20) cu. m` `= 750 cu. metres.`
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