Basic Engineering Mathematics, Fifth Edition

The circle 235

3. The perimeter of a circle is 150mm. Find its
   area, correct to the nearest square millimetre.


4. Find the area of the sector, correct to the
   nearest square millimetre, of a circle having
   a radius of 35mm with angle subtended at
   centre of 75◦.


5. An annulus has an outside diameter of
   49.0mm and an inside diameter of 15.0mm.
   Find its area correct to 4 significant figures.


6. Find the area, correct to the nearest square
   metre, of a 2m wide path surrounding a
   circular plot of land 200m in diameter.


7. A rectangular park measures 50m by 40m.
   A 3m flower bed is made round the two
   longersidesandoneshort side.Acircularfish
   pond of diameter 8.0m is constructed in the
   centre of the park. It is planned to grass the
   remaining area. Find, correct to the nearest
   square metre, the area of grass.


8. Withreference to Figure26.10, determine (a)
   the perimeter and (b) the area.

17cm

28cm

Figure 26.10

9. Find the area of the shaded portion of
   Figure 26.11.

10m

Figure 26.11

10. Find the length of an arc of a circle of radius
    8.32cm when the angle subtended at the cen-
    tre is 2.14 radians. Calculate also the area of
    the minor sector formed.


11. If the angle subtended at the centre of a cir-
    cle of diameter 82mm is 1.46rad, find the
    lengthsof the (a) minorarc and (b) major arc.


12. A pendulum of length 1.5m swings through
    an angle of 10◦in a single swing. Find, in
    centimetres, the length of the arc traced by
    the pendulum bob.


13. Determine the length of the radius and cir-
    cumference of a circle if an arc length of
    32.6cm subtends an angle of 3.76 radians.


14. Determine the angle of lap, in degrees and
    minutes, if 180mm of a belt drive are in
    contact with a pulley of diameter 250mm.


15. Determine the number of complete revo-
    lutions a motorcycle wheel will make in
    travelling 2km if the wheel’s diameter is
    85.1cm.


16. A floodlightat a sports groundspread its illu-
    mination over an angle of 40◦to a distance
    of 48m. Determine (a) the angle in radians
    and (b) the maximum area that is floodlit.


17. Find the area swept out in 50 minutes by the
    minutehand of a large floral clock if thehand
    is 2m long.


18. Determine(a)theshadedareainFigure26.12
    and (b) thepercentageof thewholesector that
    the shaded area represents.

0.75 rad 50mm

12mm

Figure 26.12