Chapter 13 Surface Areas and Volumes Ex 13.6 Solutions
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? (1000cm³ =1 L.)
Answer - 1 : -
Letthe radius of the cylindrical vessel be r.
Height (h)of vessel = 25 cm
Circumference of vessel = 132 cm
2πr =132 cmVolumeof cylindrical vessel = πr2h
=34650 cm3
= 34.65 litres
Therefore, such vessel can hold 34.65 litresof water.
Answer - 2 : - Inner radius (r1) of cylindrical pipe = 
Outer radius (r2) of cylindrical pipe =
Height(h)of pipe = Length of pipe = 35 cm
Volume of pipe =
Massof 1 cm3 wood = 0.6 g
Mass of 5720 cm3 wood = (5720 × 0.6) g
= 3432 g
= 3.432 kg
Answer - 3 : -
The tin can will be cuboidal in shape whilethe plastic cylinder will be cylindrical 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
Radius (r)of circular end of plastic cylinder =
Height(H)of plastic cylinder = 10 cm
Capacity of plasticcylinder = πr2H
Therefore, plastic cylinder has the greatercapacity.
Difference incapacity = (385 − 300) cm3 = 85 cm3
Question - 4 : - Ifthe lateral surface of a cylinder is 94.2 cm2 andits height is 5 cm, then find (i) radius of its base (ii) its volume. [Use π =3.14]
Answer - 4 : -
(i)Height (h)of cylinder = 5 cm
Let radius ofcylinder be r.
CSA of cylinder =94.2 cm2
2πrh =94.2 cm2
(2 × 3.14 × r ×5) cm = 94.2 cm2
r = 3 cm
(ii) Volume ofcylinder = πr2h
= (3.14 × (3)2 × 5) cm3
= 141.3 cm3
Question - 5 : - Itcosts Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 mdeep. 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 - 5 : -
(i)Rs 20 is the cost of painting 1 m2 area.
Rs 2200 is the costof painting =
= 110m2 area
Therefore, the innersurface area of the vessel is 110 m2.
(ii) Let the radiusof the base of the vessel be r.
Height (h)of vessel = 10 m
Surface area = 2πrh =110 m2
(iii)Volume of vessel = πr2h
=96.25 m3
Therefore, thecapacity of the vessel is 96.25 m3 or 96250 litres.
Answer - 6 : -
Letthe radius of the circular end be r.
Height (h)of cylindrical vessel = 1 m
Volume of cylindricalvessel = 15.4 litres = 0.0154 m3
⇒ r = 0.07 m
Therefore,0.4708 m2 of the metal sheet would be required to makethe cylindrical vessel.
Question - 7 : - A lead pencil consists of a cylinder of wood with solid cylinder ofgraphite filled in the interior. The diameter of the pencil is 7 mm and thediameter of the graphite is 1 mm. If the length of the pencil is 14 cm, findthe volume of the wood and that of the graphite.
Answer - 7 : - 
Radius (r1) of pencil =
=0.35 cm Radius (r2) of graphite =
=0.05 cmHeight (h)of pencil = 14 cm
Volume of wood inpencil =
Question - 8 : - A patient in a hospital is given soup daily in a cylindrical bowl ofdiameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how muchsoup the hospital has to prepare daily to serve 250 patients?
Answer - 8 : - 
Radius (r)of cylindrical bowl = Height(h)of bowl, up to which bowl is filled with soup = 4 cm
Volume of soup in 1bowl = πr2h
= (11× 3.5 × 4) cm3
= 154 cm3
Volume of soup givento 250 patients = (250 × 154) cm3
= 38500 cm3
= 38.5 litres.