Question 1: The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 cm^{3} = 1l)

**Answer:** Given: circumference = 132 cm, h = 25 cm

Circumference `=2πr`

Or, `132=2πr`

Or, `r=(132xx7)/(2xx22)=21` cm

Volume of cylinder `=πr^2\h=(22)/7xx21^2xx25`

= 34650 cubic cm `=(34650)/(1000)` litre = 34.65 litre

Question 2: The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm^{3} of wood has a mass of 0.6 g.

**Answer:** Given: R = 14 cm, r = 12 cm, h = 35 cm

Volume of pipe `=πR^2\h–πr^2\h`

`=πh(R^2-r^2)`

`=(22)/7xx35(14^2-12^2)`

`=110(14+12)(14–12)`

`=110xx26xx2=5720` cubic cm

Mass `=5720xx0.6` g = 3432 g

Question 3: A soft drink is available in two packs – (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and (ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?

**Answer:** Rectangular can: `l=5` cm, b=4` cm, h=15` cm

Volume of cubcoid `=l\xx\b\xx\h`

`=5xx4xx15=300` cubic cm

Cylindrical can: r = 35 cm, h = 10 cm

Volume of cylinder `=πr^2h`

`=(22)/7xx35^2xx10` = 385 cubic cm

Difference = 385 – 300 = 85 cubic cm

Question 4: If the lateral surface of a cylinder is 94.2 cm^{2} and its height is 5 cm, then find (i) radius of its base (ii) its volume. (Use π = 3.14)

**Answer:** Given: curved surface area of cylinder = 94.2 sq cm, h = 5 cm

CSA of cylinder `=2πrh`

Or, `94.2=2xx3.14xx\r\xx5`

Or, `r=(94.2)/(2xx3.14xx5)=3` cm

Now, volume of cylinder `=πr^2h`

`=3.14xx3^2xx5=141.30` cubic cm

Question 5: It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per m^{2}, find

(i) inner curved surface area of the vessel,

(ii) radius of the base,

(iii) capacity of the vessel.

**Answer:** Cost = Rs. 2200, rate = Rs. 20 per sq m, h = 10 m

Curved surface area = Cost ÷ Rate

`=(2200)/(20)=110` sq cm

CSA of cylinder `=2πrh`

Or, `110=2xx(22)/7xx\r\xx10`

Or, `r=(110xx7)/(2xx22xx10)=1.75` cm

Now, volume of cylinder `= πr^2h`

`=(22)/7xx1.75^2xx10=96.25` cubic m

Question 6: The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?

**Answer:** Capacity = 15.4 litre = 15400 cubic cm, h = 1 m = 100 cm

Volume of cylinder `=πr^2h`

Or, `15400=(22)/7xx\r^2xx100`

Or, `r^2=(15400xx7)/(22xx100)=49`

Or, `r=7` cm

Now, total surface area of cylinder `=2πr(r+h)`

`=2xx(22)/7xx7(7+10)`

`=2xx22xx17=748` sq cm

Question 7: A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.

**Answer:** Radius of pencil = 3.5 mm, h = 14 cm = 140 mm

Volume of pencil `=πr^2h`

`=(22)/7xx3.5^2xx140=5390` cubic mm

Radius of lead = 0.5 mm, h = 140 mm

Volume of lead `=πr^2h`

`=(22)/7xx0.5^2xx140=110` cubic mm

Hence, volume of wood = 5390 – 110 = 5280 cubic mm

Question 8: A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?

**Answer:** Given: r = 3.5 cm, h = 4 cm

Volume of cylinder `=πr^2h`

`=(22)/7xx3.5^2xx4=154` cubic cm

Volume of 250 bowls `=250xx154=38500` cubic cm = 38.5 litre

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