Ex - 13.6
Question 1. Assume
, unless stated otherwise.
The circumference of the base of cylindrical vessel is 132 cm and its height is 25 cm. How, many litres of water can it holds? (1000 cm3= 1l)
Solution
Height (h) of pencil = 14 cm
Volume of wood in pencil =
Question 1. Assume
, unless stated otherwise.The circumference of the base of cylindrical vessel is 132 cm and its height is 25 cm. How, many litres of water can it holds? (1000 cm3= 1l)
Solution
Let the radius of the cylindrical vessel be r.
Height (h) of the vessel = 25 cm
Circumference of the vessel = 132 cm
2
r = 132 cm
Height (h) of the vessel = 25 cm
Circumference of the vessel = 132 cm
2
r = 132 cm
Volume of cylindrical vessel = r2h
r2h
Thus, the vessel can hold 34.65 litres of water.
Question 2. Assume 
, unless stated otherwise.
, unless stated otherwise.
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.
Solution
Inner radius (r1) of cylindrical pipe = 
Outer radius (r2) of cylindrical pipe = 
Height (h) of pipe = Length of pipe = 35 cm
Volume of pipe =
Volume of pipe =
Mass of 1 cm3 wood = 0.6 g
Mass of 5720 cm3 wood = 5720
0.6 g = 3432 g = 3.432 kg
Mass of 5720 cm3 wood = 5720
0.6 g = 3432 g = 3.432 kg
Question 3. Assume 
, unless stated otherwise.
, unless stated otherwise.
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?
Solution
The tin can will be cuboidal in shape.
Length (l) of tin can = 5 cm
Breadth (b) of tin can = 4 cm
Height (h) of tin can = 15 cm
Capacity of tin can = l
b h = (5 4 15) cm3 = 300 cm3
Breadth (b) of tin can = 4 cm
Height (h) of tin can = 15 cm
Capacity of tin can = l
b h = (5 4 15) cm3 = 300 cm3
Radius (R) of circular end of plastic cylinder = 
Height (H) of plastic cylinder = 10 cm
Capacity of plastic cylinder = 
R2H =
=385 cm3
R2H ==385 cm3
Thus, the plastic cylinder has greater capacity.
Difference in capacity = (385 - 300) cm3 = 85 cm3
Difference in capacity = (385 - 300) cm3 = 85 cm3
Question 4. Assume 
, unless stated otherwise.
, unless stated otherwise.
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 
= 3.14)
= 3.14)
Solution
(i) Height (h) of cylinder = 5 cm
Let radius of cylinder be r.
CSA of cylinder = 94.2 cm2
2rh = 94.2 cm2
(2
3.14 r 5) cm = 94.2 cm2
r = 3 cm
Let radius of cylinder be r.
CSA of cylinder = 94.2 cm2
2
rh = 94.2 cm2(2
3.14 r 5) cm = 94.2 cm2r = 3 cm
(ii) Volume of cylinder = r2h = (3.14 (3)2 5) cm3 = 141.3 cm3
r2h = (3.14 (3)2 5) cm3 = 141.3 cm3
Question 5. Assume 
, unless stated otherwise. It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10m deep. If the cost of painting is at the rate of Rs 20 per m2, find
, unless stated otherwise. It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10m 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
Solution
(i) Cost of painting 1 m2 area = Rs 20
So, Rs 2200 is cost of painting
area , i.e, 110 m2 area.
Thus, the inner surface area of the vessel is 110 m2.
(ii) Let radius of base of vessel be r.
Height (h) of vessel = 10 m
Surface area = 2
rh = 110 m2
So, Rs 2200 is cost of painting
area , i.e, 110 m2 area.Thus, the inner surface area of the vessel is 110 m2.
(ii) Let radius of base of vessel be r.
Height (h) of vessel = 10 m
Surface area = 2
rh = 110 m2
(iii) Capacity of vessel = r2h =
= 96.25 m3
r2h = = 96.25 m3
Question 6. Assume 
, unless stated otherwise.
, unless stated otherwise.
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?
Solution
Let radius of the circular ends of the cylinder be r.
Height (h) of the cylindrical vessel = 1 m
Volume of cylindrical vessel = 15.4 litres = 0.0154 m3
Height (h) of the cylindrical vessel = 1 m
Volume of cylindrical vessel = 15.4 litres = 0.0154 m3
Total Surface area of vessel = 2
r(r+h)
r(r+h)
Thus, 0.4708 m2 of metal sheet would be needed to make the cylindrical vessel.
Question 7. Assume 
, unless stated otherwise.
, unless stated otherwise.
A lead pencil consists of a cylinder of wood with 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.
Solution
Radius (r1) of pencil = 
= 0.35 cm
Radius (r2) of graphite =
= 0.35 cmRadius (r2) of graphite =
Height (h) of pencil = 14 cm
Volume of wood in pencil =
Volume of Graphite = 
= 0.11 cm3
Question 8. Assume 
, unless stated otherwise.
, unless stated otherwise.
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?
Solution
Radius (r) of cylindrical bowl = 
cm = 3.5 cm
Height (h) up to which the bowl is filled with soup = 4 cm
cm = 3.5 cmHeight (h) up to which the bowl is filled with soup = 4 cm
Volume of soup in 1 bowl = 
r2h= 
Volume of soup in 250 bowls = (250
154) cm3 = 38500 cm3 = 38.5 litres
Thus, the hospital will have to prepare 38.5 litres of soup daily to serve 250 patients.
r2h= Volume of soup in 250 bowls = (250
154) cm3 = 38500 cm3 = 38.5 litresThus, the hospital will have to prepare 38.5 litres of soup daily to serve 250 patients.
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