Basic Engineering Mathematics, Fifth Edition

228 Basic Engineering Mathematics his calculated using Pythagoras’ theorem: 82 =h^2 + 42 from which h= √ 82 − 42 = 6 .928cm Henc ...

Areas of common shapes 229 (a) its area in hectares (1 ha= 104 m^2 ). (b) the length of fencing required, to the near- est metre ...

Chapter 26 The circle 26.1 Introduction Acircleis aplain figureenclosed by acurved line,every point on which is equidistantfrom ...

The circle 231 is greater than a semicircle it is called amajor segment(see the un-shaded area in Figure 26.2). (k) Anarcis a po ...

232 Basic Engineering Mathematics Calculate the length of wire in the paper clip shown in Figure 26.6. The dimensions are in mi ...

The circle 233 Convert to degrees: (a) 7 π 6 rad (b) 4 π 9 rad (c) 7 π 12 rad Convert to degrees and minutes: (a) 0.0125rad ( ...

234 Basic Engineering Mathematics (b) Length of major arc=(circumference−minor arc)= 2 π( 8. 4 )− 18. 3 =34.5cm, correct to 3 si ...

The circle 235 The perimeter of a circle is 150mm. Find its area, correct to the nearest square millimetre. Find the area of th ...

236 Basic Engineering Mathematics Determine the length of steel strip required to make the clip shown in Figure 26.13. 125mm r ...

The circle 237 x^2 +y^2 + 8 x− 2 y+ 8 =0 is of the form shown in equation (2), where a=− ( 8 2 ) =− 4 ,b=− ( − 2 2 ) = 1 and r= ...

Revision Test 10 : Areas and circles This assignment covers the material contained in Chapters 25 and 26.The marks available are ...

Revision Test 10 : Areas and circles 239 determine the true area of the land in hectares (1 hectare= 104 m^2 ). (4) Determine t ...

Chapter 27 Volumes of common solids 27.1 Introduction Thevolumeof any solid is a measure of the space occu- pied by the solid. V ...

Volumes of common solids 241 (a) Volume of oil tank=volume of cube = 1 .5m× 1 .5m× 1 .5m = 1. 53 m^3 =3.375m^3 1m^3 =100cm×100cm ...

242 Basic Engineering Mathematics Outer diameter,D=25cm= 0 .25m and inner diame- ter,d=12cm= 0 .12m. Area of cross-section of co ...

Volumes of common solids 243 Total surface area=area of each end+area of three sides. In triangleABC, AC^2 =AB^2 +BC^2 from whic ...

244 Basic Engineering Mathematics The volume of a cylinder is 75cm^3. If its height is 9.0cm, find its radius. Calculate the vo ...

Volumes of common solids 245 5cm 5cm D C E A B Figure 27.10 The total surface area consists of a square base and 4 equal triangl ...

246 Basic Engineering Mathematics Alternatively, fromthe question,r=30mm=3cmand h=80mm=8cm. Hence, volume= 1 3 πr^2 h= 1 3 ×π× 3 ...

Volumes of common solids 247 A sphere has a diameter of 6cm. Determine its volume and surface area. If the volume of a sphere i ...