Area & Volume
 

  1. Question: A `4 cm` cube is cut into `1` cm cubes. The total surface area of all the small cubes is ;

    A
    `96 cm^2`

    B
    `24 cm^2`

    C
    `384 cm^`

    D
    None

    Note: Number of cubes `= ((4 xx 4 xx 4)/(1 xx 1 xx 1))` `= 64.` Surface area of all small cubes `= 64 xx [6 xx (1)^2]` `= 384 cm^2.`
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  2. Question: If the area of three adjacent faces of a rectangular block are in the ratio of `2 : 3 : 4` and its volume is `9000 cu ; then the length of the shortest side is :

    A
    `10 cm`

    B
    `15 cm`

    C
    `20 cm`

    D
    `30 cm`

    Note: Let lb`= 2x,` bh`= 3x` and lh`= 4x.` Then,` 24x^3 = (lbh)^2` `= 9000 xx 9000` `:. x^3 = 375 xx 9000` `or x = 150.` :. `lb = 300`, `bh = 450 & lh = 600 & lbh = 9000.` `:. h = 9000/300 30,` `l = 9000/450` `= 20 & b = 9000/600 = 15.` :. Shortest side`= 15 cm.`
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  3. Question: The percentange increase in the surface area of a cube when each side is doubled, is :

    A
    `25%`

    B
    `50%`

    C
    `150%`

    D
    `300%`

    Note: Let the edge of the cube be a. Then, new edge`= 2a`. Original surface area`= 6a^2,` New surface area `= 6 xx (2a)^2` `= 24a.^2` :. Increase in surface area `= ((18a^2)/(6a^2) xx 100)%` `= 300%.`
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  4. Question: If the diameter of a cylinder is `28` cm and its height is `20 cm,`then total surface area is :

    A
    `2993 cm^2`

    B
    `2992 cm^2`

    C
    `2292 cm^2`

    D
    `2229 cm^2`

    Note: Total surface area `= (2π rh + 2 π r^2) cm^2` `=(2 xx 22/7 xx 14 xx 20 + 2 xx 22/7 xx 14 xx 14) cm^2` `= 2992 cm^2.`
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  5. Question: The volume of cylinder whose height is `84 cm` and the diameter base `5 cm` is :

    A
    `1320 cm^3`

    B
    `1650 cm^3`

    C
    `3300 cm^3`

    D
    `1339.64 cm^3`

    Note: Volume `= π r^2 h = (22/7 xx 5/2 xx 5/2 xx 84) cm^3` `= 1650 cm^3`
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  6. Question: If the curved surface area of a cylinder is `1760 sq`. cm and its base radius is `14 cm`, then its volume is :

    A
    `12320 cm^3`

    B
    `6160 cm^3`

    C
    `77440 cm^3`

    D
    None

    Note: `(2π rh)/r` `= 1760/14 ⇒ h` `= 1760/14 xx 1/(2π)` `= (1760/14 xx 1/2 xx 7/22)` `20 cm.` :. Volume`=π r^2 h` `= (22/7 xx 14 xx 14 xx 20) cm^3` `= 12320 cm^3.`
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  7. Question: The height of a cylinder is `14` cm and its curved surface area is `704` sq. cm, then its volume is :

    A
    `2816 cm^3`

    B
    `5632 cm^3`

    C
    `1408 cm^3`

    D
    `9856 cm^3`

    Note: `(2πrh)/h` `= 704/14 ⇒ 2π r = 704/14.` `:. r = (704/14 xx 1/2 xx 7/22) = 8 cm.` :. Volume`= (22/7 xx 8 xx 8 xx 14) cm^3` `= 2816 cm^3.`
    1. Report

  8. Question: The curved surface area of a cylinder is `2640` sq. cm and the circumference of its base is `66` cm. The volume of the cylinder is :

    A
    `174240 cm^3`

    B
    `6930 cm^3`

    C
    `13860 cm^3`

    D
    `27620 cm^3`

    Note: `(2πrh)/(2πr)` `= (2640/66) ⇒ r` `= (66 xx 1/2 xx 7/22) = 21/2 cm.` `(2πrh)/(2πr)` `= (2640/66) ⇒ h` `= 40 cm.` :. Volume `= (22/7 xx 21/2 xx 21/2 xx 40) cm^3` `= 13860 cm^3.`
    1. Report

  9. Question: The curved surface area of a right circular cylinder of base radius r is obtained by multiplying its volume by :

    A
    `2r`

    B
    `2/r`

    C
    `2r^2`

    D
    `2/r^2`

    Note: Curved surface Area `= 2πrh` `= (πr^2h). 2/r` `= (Volume xx 2/r)`
    1. Report

  10. Question: A copper sphere of radius `3` cm is beaten and drawn into a wire of diameter `0.2 cm.` The length of the wire is :

    A
    `9 m`

    B
    `12 m`

    C
    `18 m`

    D
    `36 m`

    Note: Volume of sphere = Volume of wire `:. 4/3 π xx (3)^3` `= π xx (0.1)^2 xx h` `= 36/.01 cm` `= 3600 cm` `= 36 m.`
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