244 Basic Engineering Mathematics
- The volume of a cylinder is 75cm^3. If its
height is 9.0cm, find its radius. - 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. - The volume of a cylinder is 400cm^3 .If
its radius is 5.20cm, find its height. Also
determine its curved surface area. - 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. - 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. - 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. - How long will it take a tap dripping at a rate
of 800mm^3 /s to fill a 3-litre can? - 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. - How much concrete is required for the con-
struction of the path shown in Figure 27.8, if
the path is 12cm thick?
2m1.2m8.5m2.4m3.1mFigure 27.827.2.4 Pyramids
Volume of any pyramid=1
3×area of base×perpendicular heightA 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
3x^2 hhxxFigure 27.9Problem 9. A square pyramid has a
perpendicular height of 16cm. If a side of the base
is 6cm, determine the volume of a pyramidVolume of pyramid=1
3×area of base×perpendicular height=1
3×( 6 × 6 )× 16=192cm^3Problem 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