Basic Engineering Mathematics, Fifth Edition

248 Basic Engineering Mathematics 3m r r (^5) 8cm 12cm Figure 27.14 (a) The section of wood is a prism whose end com- prises a r ...

Volumes of common solids 249 Total surface area of pyramid = 2 ( 26. 80 )+ 2 ( 39. 83 )+( 3. 60 )( 5. 40 ) = 53. 60 + 79. 66 + 1 ...

250 Basic Engineering Mathematics Hence, the volume of (hemisphere+cone) = 0. 92 × 540 πcm^3 i.e.^1 2 ( 4 3 πr^3 ) + 1 3 πr^2 h= ...

Volumes of common solids 251 Curved surface area of cylinder, Q= 2 πrh = 2 ×π× 3 × 8 = 48 πm^2 The slant height of the cone,l, i ...

252 Basic Engineering Mathematics Find the volume (in cm^3 ) of the die-casting shown in Figure 27.19. The dimensions are in mi ...

Volumes of common solids 253 4.0cm P E A D B R Q C 2.0cm 3.6cm 1.0cm 3.0cm 6.0cm Figure 27.22 The height of the large cone= 3. 6 ...

254 Basic Engineering Mathematics Problem 26. A storage hopper is in the shape of a frustum of a pyramid. Determine its volume i ...

Volumes of common solids 255 r= 5 .0cm,R= 10 .0cm and l= √[ 25. 02 + 5. 02 ] = 25 .50cm from Pythagoras’ theorem. Hence, curved ...

256 Basic Engineering Mathematics 27.6 Volumes of similar shapes Figure 27.27 shows two cubes, one of which has sides three time ...

Chapter 28 Irregular areas and volumes, and mean values 28.1 Areas of irregular figures Areas of irregular plane surfaces may be ...

258 Basic Engineering Mathematics (i) Divide baseADinto any number of equal intervals, each of widthd(the greater the number of ...

Irregular areas and volumes, and mean values 259 Now try the following Practice Exercise Practice Exercise 110 Areas of irregula ...

260 Basic Engineering Mathematics 16400m^3 = 16400 × 106 cm^3. Since 1 litre=1000cm^3 , capacity of reservoir= 16400 × 106 1000 ...

Irregular areas and volumes, and mean values 261 Problem 5. Determine the average values over half a cycle of the periodic wavef ...

262 Basic Engineering Mathematics Problem 7. The power used in a manufacturing process during a 6 hour period is recorded at int ...

Irregular areas and volumes, and mean values 263 been divided into 6 equally spaced intervals and the lengths of the 7 ordinates ...

Revision Test 11 : Volumes, irregular areasand volumes, and mean values This assignment covers the material contained in Chapter ...

Revision Test 11 : Volumes, irregular areas and volumes, and mean values 265 Plot a graph ofy= 3 x^2 +5 fromx=1tox=4. Estimate, ...

Chapter 29 Vectors 29.1 Introduction This chapter initially explains the difference between scalar and vector quantities and sho ...

Vectors 267 at 45◦to the horizontal is shown in Figure 29.1. Note that an angle of+ 45 ◦is drawn from the horizontal and movesan ...