The circumferences of circular faces of a frustum are 132 cm and 88 cm and its height is 24 cm. To find the curved surface area of the frustum complete the following activity. ( = 22/7 ).
Circumference1 = 2r1 = 132r1 = 132/2 = 21cm [=22/7]Circumference2 = 2r2 = 88r2 = 88/2 = 14cmSlant height of frustum l = √[h2+(r1-r2)2]= √[242+(21-14)2] [given h =24]= √[576+(7)2]= √[576+49]= √625= 25cmCurved surface area of frustum = (r1+r2)l= ×(21+14)×25= ×(35)×25= 2750sq.cm
The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its
Given r1 = 14cmr2= 6cmHeight , h = 6cmSlant height of frustum l = √[h2+(r1-r2)2]= √[62+(14-6)2]= √[36+(8)2]= √[36+64]= √100 = 10 (i) Curved surface area of frustum = l(r1+r2)= ×10(14+6)= ×10×20= 3.14 ×200= 628cm2Hence curved surface area of frustum is 628cm2. (ii) Total surface area of frustum = l (r1+ r2)+r12+r22= ×10(14+ 6)+×142+×62= ×10×20+×196+×36= 200+196+36= 432= 432×3.14= 1356.48cm2Hence Total surface area of frustum […]
The radii of two circular ends of frustum shape bucket are 14 cm and 7 cm. Height of the bucket is 30 cm. How many liters of water it can hold ? (1 litre = 1000 cm3 )
Given height of bucket , h = 30cmr1 = 14cmr2= 7cmVolume of a frustum = (1/3)h(r12+r22+r1×r2)Volume of bucket = (1/3)×30(142+72+14×7)= 10×(196+49+98)= 3430= 10780cm3= 10.78 litres [∵1 litre = 1000 cm3 ]Hence the bucket can hold 10.78 litres of water.