Volume of Cylinder

Exercise 13.6

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 cm3 = 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 cm3 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`




`=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 cm2 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 m2, 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)`


`=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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