# 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 = 2 π r
Or, 132 = 2 πr
Or, r = (132 xx7)/(2 xx 22) = 21 cm

Volume of cylinder = π r^2\h= (22/7) xx 21^2\ xx 25
= 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 = π R^2\h – π r^2\h
= π h (R^2\ - r^2)
= (22/7) xx 35 (14^2 - 12^2)
= 110 (14 + 12)(14 – 12)
= 110 xx 26 xx 2 = 5720 cubic cm
Mass = 5720 xx 0.6\ 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
= 5 xx 4 xx 15 = 300 cubic cm

Cylindrical can: r = 35 cm, h = 10 cm
Volume of cylinder = π r^2\ h
= (22/7) xx 35^2\xx 10
= 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 = 2 π rh
Or, 94.2 = 2 xx 3.14 xx r xx 5
Or, r = 94.2/(2 xx 3.14 xx 5) = 3 cm

Now, volume of cylinder = π r^2\ h
= 3.14 xx 3^2\ xx 5 = 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 = 2 π rhOr, 110 = 2 xx (22/7) xx r xx 10
Or, r = (110 xx 7)/(2 xx 22 xx 10) = 1.75 cm

Now, volume of cylinder = π r^2\ h
= (22/7) xx (1.75)^2\ xx 10 = 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 = π r^2\ h
Or, 15400 = (22/7) xx r^2\xx 100
Or, r^2= (15400 xx 7)/(22 xx 100) = 49
Or, r = 7 cm

Now, total surface area of cylinder = 2 π r(r + h)
= 2 xx (22/7) xx 7 (7 + 10)
= 2 xx 22 xx 17 = 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 = π r^2\h
= (22/7) xx (3.5)^2\ xx 140 = 5390 cubic mm

Radius of lead = 0.5 mm, h = 140 mm
Volume of lead = π r^2\ h
= (22/7) xx (0.5)^2\ xx 140 = 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 = π r^2\ h
= (22/7) xx (3.5)^2\ xx 4 = 154 cubic cm
Volume of 250 bowls = 250 X 154 = 38500 cubic cm = 38.5 litre