Area & Volume
 

  1. Question: A cylindrical piece of metal of radius `2` cm and height `6`cm is shaped into a cone of same radius. The height of the cone is :

    A
    `8 cm`

    B
    `12 cm`

    C
    `14 cm`

    D
    `18 cm`

    Note: `π xx 2^2 xx 6` `= 1/3 π xx 2^2 xx h ⇒ h` `= 18 cm.`
    1. Report

  2. Question: If a right circular cone of height `24` cm has volume of `1232` cu. cm, then the area of its curved surface is :

    A
    `154 cm^2`

    B
    `550 cm^2`

    C
    `704 cm^2`

    D
    ` 1254 cm^2`

    Note: `1/3 πr^2 xx 24` `= 1232 ⇒ r^2` `= (154 xx 7/22)` `= 49 or r = 7 cm.` :. Slant height, `l = √(24)^2 + 7^2` `= √625` `= 25 cm.` :. Area of Curved Surface `= π rl = (22/7 xx 7 xx 25) cm^2` `= 550 cm^2.`
    1. Report

  3. Question: The length of canvas `1.1` m wide will be required to build a conical tent of height `14` m and the floor area `346.5` m is :

    A
    `525 m`

    B
    `490 m`

    C
    665 m`

    D
    `860 m`

    Note: πr^2 = 346.5 ⇒ r^2` `= 346.5 xx 7/22` `= 441/4 ⇒ r = 21/2.` :. l = √r^2 + h^2` `= √ 441/4 + (14)^2` `= √1225/4` `= 35/2` :. Area of canvas needed `= πrl = (22/7 xx 21/2 xx 35/2) m^2` `= ((33 xx 35)/2) m^2` :. Length of canvas `= ((33 xx 35)/(2 xx 1.1)) m` `= 525 m.`
    1. Report

  4. Question: How many metres of cloth `2.5` m wide will be required to make a conical tent whose base radius is`7` m and height is `24` m ?

    A
    `120 m`

    B
    `180 m`

    C
    `220 m`

    D
    `550 m`

    Note: Not available
    1. Report

  5. Question: It the volume of two cones are in the ratio of `1 : 4` and their diameters are in the ratio of ``4 : 5`, then the ratio of their heights is :

    A
    `1 : 5`

    B
    `5 : 4`

    C
    `5 : 16`

    D
    `25 : 64`

    Note: Let their ratio be `4x & 5x & heights be h & H. Then,`(1/3 π(4x)^2 xx h)/(1/3 π (5x)^2 xx h)` `1/4 or h/H = 1/4 xx 25/16` `= 25/64`
    1. Report

  6. Question: Volume of a hemisphere is `19404 cu`. cm. Its radius is :

    A
    `10.5 cm`

    B
    `21 cm`

    C
    `17.5 cm`

    D
    `42 cm`

    Note: `2/3 xx 22/7 xx R^3` `= 19404 ⇒ R^3` `= (19404 xx 21/44)` `= (21)^3` `or = 21 cm.`
    1. Report

  7. Question: A well with `14` m inside diameter is dug `10` m deep. Earth taken out of it has been evenly spread all around it to a which of `21` m to form n embankment. The height of the embankment is :

    A
    `1/2 m`

    B
    `2/3 m`

    C
    `3/4 m`

    D
    3/5 m`

    Note: Volume of earth dug out `= (22/7 xx 7 xx 10) m^2` `= 1540 m^2. Area of embankment `= 22/7 xx [(28)^2 - (7)^2]` `= (22/7 xx 35 xx 21) m^2` `= 2310 m^2` Height of embankment `((volume)/(Area))` `= (1540/2310) m` `= 2/3 m.`
    1. Report

  8. Question: The radii of the base of a cylinder and a cone are in the ratio of `3 : 4` and their heights are in the ratio `2 : 3`. Their volumes are in the ratio of :

    A
    `9 : 8`

    B
    `3 : 4`

    C
    `8 : 9`

    D
    `4 : 3`

    Note: Let their radii be `3x, 4x & heights be `2x` and `3x`. Ratio of their volumes `= (π xx (3x)^2 xx 2x)/(1/3 π xx (4x)^2 xx 3x)` `= 18/16` `= 9/8`
    1. Report

  9. Question: A cylindrical vessel `32` cm high and `18`cm as the radius of the base is filled with sand. This is emptied on the ground and a conical head of sand is formed. If the height of the conical head is `24` cm, the radius of its base is :

    A
    `12 cm`

    B
    `24 cm`

    C
    `36 cm`

    D
    `48 cm`

    Note: `π xx 18 xx 18 xx 32` `= 1/3 π xx R^2 xx 24 ⇒R^2` `= ((18 xx 18 xx 32)/8)` :. R`= 36 cm.`
    1. Report

  10. Question: A solid metallic cylindrical of base radius `3` cm and height `5` cm is melted to form cones is ;

    A
    `45o`

    B
    `1350`

    C
    `4500`

    D
    `13500`

    Note: Volume of cylinder `= (π xx3 xx 3 xx 5) cm^3` `= (45 π) cm^3. volume of `1` cone `= (1/3 π xx 1/10 xx 1/10 xx 1)` `= π/300 cm.^3` Number of cones `= (45 π xx 300/π)` `= 13500`.
    1. Report
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