VOLUME OF CYLINDER QUESTIONS AND ANSWERS

Question 1 :

Volume of a solid cylinder is 62.37 cu.cm. Find the radius if its height is 4.5 cm

Solution :

Height of solid cylinder  =  4.5 cm

Volume of cylinder  =  62.37 cu.cm

πr2h  =  62.37

 (22/7) ⋅ r24.5  =  62.37

r2  =  62.37 ⋅ (1/4.5)  (7/22)

r2  =  13.86 ⋅ (7/22)

r2  =  97.02/22

r2  =  4.41

r  =  √(2.1 ⋅ 2.1)

r  =  2.1 cm

Radius of the cylinder  =  2.1 cm

Question 2 :

The radii of two right circular cylinders are in the ratio 2:3. Find the ratio of their volumes if their heights are in the ratio 5:3.

Solution :

Let r1 and r2 are the radii of two cylinders.

Let hand h2 are the heights of two cylinders.

rr2  =  2:3

r1/r=  2/3

r1  =  2r2/3

h1 : h2  =  5 : 3

h1/h =  5/3

h1  =  5h2/3

Volume of cylinder  =  πr2h

πr12h1 : πr22 h2

(2r2/3)2 (5h2/3) : r22 h2

 (4 r22/9)(5h2/3) : r2h2

20/27 : 1

20 : 27

Ratio of volume of two cylinders 20 : 27

Question 3 : 

The radius and height of two circular cylinders are in the ratio 5 : 7. If its volume is 4400 cu.cm, find the radius of the cylinder.

Solution :

Let r and h are the radius and height of cylinder

r : h  =  5 : 7

r/h  =  5/7

r  =  5h/7

Volume of the cylinder  =  4400 cu.cm

πr2h  =  4400

(22/7) (5h/7)2 ⋅ h = 4400

(22/7) ⋅ (25h2/49)  h  =  4400

h3 = 4400 ⋅ (7/22) ⋅ (49/25)

h3  =  176 ⋅ (7/22) ⋅ 49

h3  =  8 ⋅ 7 ⋅ 7 ⋅ 7

h  =  14 cm

r  =  5(14)/7

r  =  10 cm

Radius of the cylinder = 10 cm.

Question 4 :

A rectangular sheet of metal foil with dimension 66 cm x 12 cm is rolled to form a cylinder of height 12 cm. Find the volume of the cylinder.

Solution :

Length of metal sheet  =  66 cm

Width of sheet = 12 cm

Circumference of the base of the cylinder  =  66 cm

2πr  =  66

⋅ (22/7) ⋅ r  =  66

r  =  66 ⋅ (1/2) ⋅ (7/22) 

r  =  3 ⋅ (1/2) ⋅ 7

r  =  21/2

r  =  10.5 cm

Volume of the right circular cylinder  =  πr2h

=  (22/7) ⋅ (10.5)⋅ 12

=  (22/7) ⋅ 10.5 ⋅ 10.5 ⋅ 12

=  4158 cm3

Volume of the the right circular cylinder = 4158 cm3

Question 5 :

A lead pencil is in the shape of right circular cylinder. The pencil is 28 cm long and its radius is 3 mm. If the lead is of radius 1 mm, then find the volume of the wood used in the pencil.

Solution :

Height of the pencil = 28 cm

Outer radius (R)  =  3 mm

Inner radius (r)  =  1 mm

Now we have to change the units from mm to cm. For that we have to divide it by 10.

R  =  3/10  =  0.3 cm

r  =  1/10

r  = 0.1 cm

To find the volume of the wood used to make that pencil, simply we can find the volume of the pencil. Pencil is in the shape of hollow cylinder

Volume of hollow cylinder  =  πh(R2-r2)

=   (22/7)  28  (0.32-0.12)

=  22  4  (0.09-0.01)

=  7.04 cm3

Volume of wood used in the pencil  =  7.04 cm3.

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