Area
 

  1. Question: The are of a circle is 38.5 sq.cm. Its circumference is :

    A
    `6.2 cm`

    B
    `11 cm`

    C
    `22 cm`

    D
    `121 cm`

    Note: `r^2 = 38.5 => r^2` `= (38.5 xx 7/22)` `= (7/2)^2 or r = 7/2` :. Circumference `= 2 r = (2 xx 22/7 xx 7/2) cm` `= 22 cm.`
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  2. Question: The difference between the circumference and the radius of a circle is 37 cm. The area of the circle is :

    A
    `111 cm^2`

    B
    `148 cm^2`

    C
    `154 cm^2`

    D
    `259 cm^2`

    Note: `2 r - r = 37 or (2 - 1) r = 37` `or (2 xx 22/7 - 1) r = 37 or (37r)/7` `= 37 or r = 7.` :. Area` = r^2 = (22/7 xx 7 xx 7) cm^2` `= 154 cm^2`
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  3. Question: The areas of two concentric circles forming a ring are 154 sq. and 616 sq.cm. The breadth of the ring is :

    A
    `7 cm`

    B
    `14 cm`

    C
    `21 cm`

    D
    `28 cm`

    Note: Let inner radius = r & outer radius = R. Then,`22/7 xx r^2 = 154 or r^2` `= (154 xx 7/22).` So, r = 7. Also,` 22/7 xx R^2 = 616 or R^2` `= (616 xx 7/22) or R = 14` :. Breadth of the ring `= (R - r) = (14 - 7) = 7 cm.`
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  4. Question: The circumference of two concentric circles forming a ring are 88 cm and 66 cm respectively. The width of the ring is :

    A
    `3.5 cm`

    B
    `10.5 cm`

    C
    `7 cm`

    D
    `14 cm`

    Note: Let, inner radius = r & outer radius = R cm. Then,` 2 xx 22/7 xx R = 88 => R` `= (88 xx 7/44)` `= 14 cm.` ` 2 xx 22/7 xx r = 66 => r` `= (66 xx 7/44)` `= 21/2 cm` `= 10.5 cm.` :. width of the ring `= (14 - 10.5) cm` `= 3.5 cm.`
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  5. Question: A circular road runs round a circular ground. If the difference between the circumference of the outer circle and inner circle is 66 metres, the width of the road is :

    A
    `5.25 m`

    B
    `7 m`

    C
    `10.5 m`

    D
    `21 m`

    Note: `2 (R - r) = 60 => 2 xx 22/7 xx (R - r) = 60` `:. (R - r) = (66 xx 7/44)` `= 10.5 m.`
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  6. Question: The diameter of a wheel is 1.26 m. How far will it travel in 500 revolutions ?

    A
    2530 m

    B
    1980 m

    C
    1492 m

    D
    2880 m

    Note: Radius of the wheel = 0.63 m. Distance moved in 1 revolution = circumference `= (2 xx 22/7 xx 0.63) m` `= 3.96 m.` Distance moved in 500 revolutions `= (500 xx 3.96) m` `= 1980 m`
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  7. Question: The radius of a wheel is 7 cm. How many revolutions will it make in moving 44 km ?

    A
    2000

    B
    10000

    C
    70000

    D
    100000

    Note: Distance covered in 1 revolution = circumference `= (2 xx 22/7 xx 7) cm` `= 44 cm` :.Number of revolutions made in moving 44 km `= ((44 xx 1000 xx 100)/44)` `= 100000`
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  8. Question: If the wheel of an engine of train `4 2/7` m in circumference will it make in moving 44 km ?

    A
    25 km/hr

    B
    27 km/hr

    C
    30 km/hr

    D
    35 km/hr

    Note: Distance moved in 4 sec. `= (30/7 xx 7) m` `= 30 m` :. Speed` = (30/4 xx 60 xx 60 xx 1/1000)` km/hr` = 27 km/hr.
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  9. Question: A toothed wheel of diameter 50 cm is attached to a smaller wheel of diameter 30 cm. How many revolutions will the smaller wheel make when the larger one makes 15 revolutions ?

    A
    18

    B
    20

    C
    25

    D
    30

    Note: Distance moved by toothed wheel in 15 revolutions `= (15 xx 2 xx 22/7 xx 25) cm.` Distance moved by smaller wheel in 1 revolultion `= (2 xx 22/7 xx 15) cm.` :. Required number of revolutions `= (15 xx 44/7 xx 25 xx 7)/(44 xx 15)` `= 25`
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  10. Question: The diameter of the wheel of a vehicle is 1.4 m. The wheel makes 10 revolutions in 5 seconds. The speed of the vehicle (in kmph) is :

    A
    29.46

    B
    31.68

    C
    32.72

    D
    36.25

    Note: Distance covered in 10 revolution `= (10 xx 2 xx 22/7 xx 0.7) m` `= 44 m.` Distance covered in 5 sec. `= 44 m.` Speed` = (44/5 xx 60 xx 60 xx 1/1000) kmph` `= 31.68 kmph`
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