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1.

A solid cylinder has total surface area of 462square cm. Its curved surface area is one-third of its total surface area.Find the volume of the cylinder. (Take `pi=22//7)`

Answer» `2pir(r+h)=462cm^2-(1)`
`2pirh=1/3*2pir(r+h)`
`3h=r+h`
`r=2h-(2)`
`2pi(2h)(3h)=462`
`h^2=(462*7)/(12*22)`
`h^2=12.25`
`h=3.5cm`
Volume`=22/7*7*7*3.5`
`=539cm^3`.
Discussion
2.

At a Ramzan Mela, a stall keeper in one of the food stalls has large cylindricalvessel of base radius 15cm filled up to a height of 32cm with orange juice.The juce is filled in small cylindrical glasses ofradius 3cm upto a height of 8cm, and sold for Rs. 3each. How much money does the stall keeper receive by selling the juicecompletely?

Answer» Cylinder,r=15cm,h=32cm
glass,r=3cm,h=8cm
Volume of total juice`=pir^2h`
`=pi*15*!5*32cm^3`
Volume of 1 glass`=pir^2h`
`=pi*3*3*8cm^3`
Number of glasses`=(15*15*32)/(3*3*8)=100`
Total money`=3*100=300Rs`.
Discussion
3.

The cost of painting the total outside surface ofa closed cylindrical oil tank at 50 paise persquare decimetre is Rs. 198. The height of the tank is 6 times the radius ofthe base of the tank. Find the volume corrected to 2 decimal places.

Answer» TSA`=2pirh+2pir^2`
`=12pir^2+2pr^2`
`=14pir^2`
Cost=TSA*0.5=198
`=14pir^2*0.5=198`
`r^2=9`
`r=3dm`
`h=18dm`
V=`pir^2h=3.14*9*18`
`=162*3.14dm^3`
`=508.68dm^3`.
Discussion
4.

Find the weight of a lead pipe 3.5m long, if theexternal diameter of the pipe is 2.4cm and the thickness of the lead is 2mmand 1 cubic cm of lead weighs 11gm.

Answer» Volume of lead`=pi*1.2*1.2*3.5-pi*1*1*35`
Volume`=pi(1.44*3.5-3.5)`
`=4.84cm^3`
1 `cm^3` lead weight=11gm
4.84 `cm^3` lead weight`=11*4.84`
`=532.4kg`.
Discussion
5.

A well with 14m diameter is dug 8m deep. The earthtaken out of it has been evenly spread all around it to a width of 21m toform as embankment. Find the height of the embankment.

Answer» Volume of earth taken out`=pir^2h`
`=392pi`
`r_(outer)`=21+7=28m
`r_(i n n e r)`=7cm
Volume of embankment=Volume of earth taken out
`h(pi(28^2-7^2))=392pi`
`h=0.533m`.
Discussion
6.

The circumference of the base of a cylinder is 132cm and its height 25cm. Find the volume of the cylinder.

Answer» Volume of cylinder`=pir^2h`
`2pir=132`
`r=132/(2pi)`
`r=21cm`
Volume`=22/7*21*21*25`
`=34,650cm^3`.
Discussion
7.

The ratio between the radius of the base and theheight of a cylinder is 2:3., find the total surface area of the cylinder, itits volume is `1617``c m^3dot`

Answer» `r/h=2/3`
`r=2/3h`
Volume od cylinder`=pir^2h`
`1617=22/7*2/3h*2/3h*2/3h*h`
`h^3=(1617*7*9)/(22*4)`
`h=21/2cm`
`r=7cm`
Total surface area of cylinder`=2pirh+2pir^2`
`=2*22/7(7*21/2+7*7)`
`=770cm^2`.
Discussion