Basic Engineering Mathematics, Fifth Edition

(Amelia) #1

244 Basic Engineering Mathematics



  1. The volume of a cylinder is 75cm^3. If its
    height is 9.0cm, find its radius.

  2. Calculate the volume of a metal tube whose
    outside diameter is 8cm and whose inside
    diameter is 6cm, if the length of the tube is
    4m.

  3. The volume of a cylinder is 400cm^3 .If
    its radius is 5.20cm, find its height. Also
    determine its curved surface area.

  4. A cylinder is cast from a rectangular piece of
    alloy 5cm by 7cm by 12cm. If the length of
    the cylinder is to be 60cm, find its diameter.

  5. Find the volume and the total surface area
    of a regular hexagonal bar of metal of length
    3m if each side of the hexagon is 6cm.

  6. A block of lead 1.5m by 90cm by 750mm
    is hammered out to make a square sheet
    15mm thick. Determine the dimensions of
    the square sheet, correct to the nearest cen-
    timetre.

  7. How long will it take a tap dripping at a rate
    of 800mm^3 /s to fill a 3-litre can?

  8. A cylinder is cast from a rectangular piece
    of alloy 5.20cm by 6.50cm by 19.33cm. If
    the height of the cylinder is to be 52.0cm,
    determine its diameter, correct to the nearest
    centimetre.

  9. How much concrete is required for the con-
    struction of the path shown in Figure 27.8, if
    the path is 12cm thick?


2m

1.2m

8.5m

2.4m

3.1m

Figure 27.8

27.2.4 Pyramids
Volume of any pyramid

=

1
3

×area of base×perpendicular height

A square-based pyramid is shown in Figure 27.9 with
base dimensionxbyxand the perpendicular height of
the pyramidh. For the square-base pyramid shown,

volume=

1
3

x^2 h

h

x

x

Figure 27.9

Problem 9. A square pyramid has a
perpendicular height of 16cm. If a side of the base
is 6cm, determine the volume of a pyramid

Volume of pyramid

=

1
3

×area of base×perpendicular height

=

1
3

×( 6 × 6 )× 16

=192cm^3

Problem 10. Determine the volume and the total
surface area of the square pyramid shown in
Figure 27.10 if its perpendicular height is 12cm.

Volume of pyramid

=

1
3

(area of base)×perpendicular height

=

1
3

( 5 × 5 )× 12

=100cm^3
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