# 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

=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 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,
(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

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