Scroll:Mensuration >> volume of cylinder >> ps (4129)


Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.



 

1)  

A lead pencil is in the shape of right circular cylinder. The pencil is 21cm long and its radius is  7 mm. If the lead is of radius 2mm, then find find the volume of the wood used in the pencil.

21cm
7mm
2mm(lead)
 
 
 
 
 
 


cm3


Answer:_______________




2)  

A lead pencil is in the shape of right circular cylinder. The pencil is 23cm long and its radius is  6 mm. If the lead is of radius 1mm, then find find the volume of the wood used in the pencil.

23cm
6mm
1mm(lead)
 
 
 
 
 
 


cm3


Answer:_______________




3)  

A lead pencil is in the shape of right circular cylinder. The pencil is 21cm long and its radius is  9 mm. If the lead is of radius 1mm, then find find the volume of the wood used in the pencil.

21cm
9mm
1mm(lead)
 
 
 
 
 
 


cm3


Answer:_______________




4)  

A lead pencil is in the shape of right circular cylinder. The pencil is 28cm long and its radius is  8 mm. If the lead is of radius 1mm, then find find the volume of the wood used in the pencil.

28cm
8mm
1mm(lead)
 
 
 
 
 
 


cm3


Answer:_______________




5)  

A lead pencil is in the shape of right circular cylinder. The pencil is 28cm long and its radius is  5 mm. If the lead is of radius 3mm, then find find the volume of the wood used in the pencil.

28cm
5mm
3mm(lead)
 
 
 
 
 
 


cm3


Answer:_______________




6)  

A lead pencil is in the shape of right circular cylinder. The pencil is 26cm long and its radius is  5 mm. If the lead is of radius 1mm, then find find the volume of the wood used in the pencil.

26cm
5mm
1mm(lead)
 
 
 
 
 
 


cm3


Answer:_______________




7)  

A lead pencil is in the shape of right circular cylinder. The pencil is 20cm long and its radius is  5 mm. If the lead is of radius 1mm, then find find the volume of the wood used in the pencil.

20cm
5mm
1mm(lead)
 
 
 
 
 
 


cm3


Answer:_______________




8)  

A lead pencil is in the shape of right circular cylinder. The pencil is 26cm long and its radius is  8 mm. If the lead is of radius 2mm, then find find the volume of the wood used in the pencil.

26cm
8mm
2mm(lead)
 
 
 
 
 
 


cm3


Answer:_______________




9)  

A lead pencil is in the shape of right circular cylinder. The pencil is 21cm long and its radius is  7 mm. If the lead is of radius 1mm, then find find the volume of the wood used in the pencil.

21cm
7mm
1mm(lead)
 
 
 
 
 
 


cm3


Answer:_______________




10)  

A lead pencil is in the shape of right circular cylinder. The pencil is 29cm long and its radius is  6 mm. If the lead is of radius 3mm, then find find the volume of the wood used in the pencil.

29cm
6mm
3mm(lead)
 
 
 
 
 
 


cm3


Answer:_______________




 

1)  

A lead pencil is in the shape of right circular cylinder. The pencil is 21cm long and its radius is  7 mm. If the lead is of radius 2mm, then find find the volume of the wood used in the pencil.

21cm
7mm
2mm(lead)
 
 
 
 
 
 


Answer: 29.70 cm3


SOLUTION 1 :

Given: 

Length of pencil (h) = 21cm

Radius of the pencil (R) = 7mm = 710 cm

Radius of the lead  = r = 2 mm = 210 cm

To find :  Volume of the wood used in the pencil

Solution : Volume of Hollow cylinder = πh(R + r)(R - r)

Volume of the wood in the pencil

= 227 x 21 x (  710 + 210 ) x ( 710 - 210 )

 =  66.00 x ( 910 ) x (510) cm3

= 66.00X45 / 100 cm3  =  2970 / 100  = 29.70 cm3

Volume of the wood used in the pencil is  29.70 cm3

 



2)  

A lead pencil is in the shape of right circular cylinder. The pencil is 23cm long and its radius is  6 mm. If the lead is of radius 1mm, then find find the volume of the wood used in the pencil.

23cm
6mm
1mm(lead)
 
 
 
 
 
 


Answer: 25.30 cm3


SOLUTION 1 :

Given: 

Length of pencil (h) = 23cm

Radius of the pencil (R) = 6mm = 610 cm

Radius of the lead  = r = 1 mm = 110 cm

To find :  Volume of the wood used in the pencil

Solution : Volume of Hollow cylinder = πh(R + r)(R - r)

Volume of the wood in the pencil

= 227 x 23 x (  610 + 110 ) x ( 610 - 110 )

 =  72.29 x ( 710 ) x (510) cm3

= 72.29X35 / 100 cm3  =  2530.15 / 100  = 25.30 cm3

Volume of the wood used in the pencil is  25.30 cm3

 



3)  

A lead pencil is in the shape of right circular cylinder. The pencil is 21cm long and its radius is  9 mm. If the lead is of radius 1mm, then find find the volume of the wood used in the pencil.

21cm
9mm
1mm(lead)
 
 
 
 
 
 


Answer: 52.80 cm3


SOLUTION 1 :

Given: 

Length of pencil (h) = 21cm

Radius of the pencil (R) = 9mm = 910 cm

Radius of the lead  = r = 1 mm = 110 cm

To find :  Volume of the wood used in the pencil

Solution : Volume of Hollow cylinder = πh(R + r)(R - r)

Volume of the wood in the pencil

= 227 x 21 x (  910 + 110 ) x ( 910 - 110 )

 =  66.00 x ( 1010 ) x (810) cm3

= 66.00X80 / 100 cm3  =  5280 / 100  = 52.80 cm3

Volume of the wood used in the pencil is  52.80 cm3

 



4)  

A lead pencil is in the shape of right circular cylinder. The pencil is 28cm long and its radius is  8 mm. If the lead is of radius 1mm, then find find the volume of the wood used in the pencil.

28cm
8mm
1mm(lead)
 
 
 
 
 
 


Answer: 55.44 cm3


SOLUTION 1 :

Given: 

Length of pencil (h) = 28cm

Radius of the pencil (R) = 8mm = 810 cm

Radius of the lead  = r = 1 mm = 110 cm

To find :  Volume of the wood used in the pencil

Solution : Volume of Hollow cylinder = πh(R + r)(R - r)

Volume of the wood in the pencil

= 227 x 28 x (  810 + 110 ) x ( 810 - 110 )

 =  88.00 x ( 910 ) x (710) cm3

= 88.00X63 / 100 cm3  =  5544 / 100  = 55.44 cm3

Volume of the wood used in the pencil is  55.44 cm3

 



5)  

A lead pencil is in the shape of right circular cylinder. The pencil is 28cm long and its radius is  5 mm. If the lead is of radius 3mm, then find find the volume of the wood used in the pencil.

28cm
5mm
3mm(lead)
 
 
 
 
 
 


Answer: 14.08 cm3


SOLUTION 1 :

Given: 

Length of pencil (h) = 28cm

Radius of the pencil (R) = 5mm = 510 cm

Radius of the lead  = r = 3 mm = 310 cm

To find :  Volume of the wood used in the pencil

Solution : Volume of Hollow cylinder = πh(R + r)(R - r)

Volume of the wood in the pencil

= 227 x 28 x (  510 + 310 ) x ( 510 - 310 )

 =  88.00 x ( 810 ) x (210) cm3

= 88.00X16 / 100 cm3  =  1408 / 100  = 14.08 cm3

Volume of the wood used in the pencil is  14.08 cm3

 



6)  

A lead pencil is in the shape of right circular cylinder. The pencil is 26cm long and its radius is  5 mm. If the lead is of radius 1mm, then find find the volume of the wood used in the pencil.

26cm
5mm
1mm(lead)
 
 
 
 
 
 


Answer: 19.61 cm3


SOLUTION 1 :

Given: 

Length of pencil (h) = 26cm

Radius of the pencil (R) = 5mm = 510 cm

Radius of the lead  = r = 1 mm = 110 cm

To find :  Volume of the wood used in the pencil

Solution : Volume of Hollow cylinder = πh(R + r)(R - r)

Volume of the wood in the pencil

= 227 x 26 x (  510 + 110 ) x ( 510 - 110 )

 =  81.71 x ( 610 ) x (410) cm3

= 81.71X24 / 100 cm3  =  1961.04 / 100  = 19.61 cm3

Volume of the wood used in the pencil is  19.61 cm3

 



7)  

A lead pencil is in the shape of right circular cylinder. The pencil is 20cm long and its radius is  5 mm. If the lead is of radius 1mm, then find find the volume of the wood used in the pencil.

20cm
5mm
1mm(lead)
 
 
 
 
 
 


Answer: 15.09 cm3


SOLUTION 1 :

Given: 

Length of pencil (h) = 20cm

Radius of the pencil (R) = 5mm = 510 cm

Radius of the lead  = r = 1 mm = 110 cm

To find :  Volume of the wood used in the pencil

Solution : Volume of Hollow cylinder = πh(R + r)(R - r)

Volume of the wood in the pencil

= 227 x 20 x (  510 + 110 ) x ( 510 - 110 )

 =  62.86 x ( 610 ) x (410) cm3

= 62.86X24 / 100 cm3  =  1508.64 / 100  = 15.09 cm3

Volume of the wood used in the pencil is  15.09 cm3

 



8)  

A lead pencil is in the shape of right circular cylinder. The pencil is 26cm long and its radius is  8 mm. If the lead is of radius 2mm, then find find the volume of the wood used in the pencil.

26cm
8mm
2mm(lead)
 
 
 
 
 
 


Answer: 49.03 cm3


SOLUTION 1 :

Given: 

Length of pencil (h) = 26cm

Radius of the pencil (R) = 8mm = 810 cm

Radius of the lead  = r = 2 mm = 210 cm

To find :  Volume of the wood used in the pencil

Solution : Volume of Hollow cylinder = πh(R + r)(R - r)

Volume of the wood in the pencil

= 227 x 26 x (  810 + 210 ) x ( 810 - 210 )

 =  81.71 x ( 1010 ) x (610) cm3

= 81.71X60 / 100 cm3  =  4902.6 / 100  = 49.03 cm3

Volume of the wood used in the pencil is  49.03 cm3

 



9)  

A lead pencil is in the shape of right circular cylinder. The pencil is 21cm long and its radius is  7 mm. If the lead is of radius 1mm, then find find the volume of the wood used in the pencil.

21cm
7mm
1mm(lead)
 
 
 
 
 
 


Answer: 31.68 cm3


SOLUTION 1 :

Given: 

Length of pencil (h) = 21cm

Radius of the pencil (R) = 7mm = 710 cm

Radius of the lead  = r = 1 mm = 110 cm

To find :  Volume of the wood used in the pencil

Solution : Volume of Hollow cylinder = πh(R + r)(R - r)

Volume of the wood in the pencil

= 227 x 21 x (  710 + 110 ) x ( 710 - 110 )

 =  66.00 x ( 810 ) x (610) cm3

= 66.00X48 / 100 cm3  =  3168 / 100  = 31.68 cm3

Volume of the wood used in the pencil is  31.68 cm3

 



10)  

A lead pencil is in the shape of right circular cylinder. The pencil is 29cm long and its radius is  6 mm. If the lead is of radius 3mm, then find find the volume of the wood used in the pencil.

29cm
6mm
3mm(lead)
 
 
 
 
 
 


Answer: 24.61 cm3


SOLUTION 1 :

Given: 

Length of pencil (h) = 29cm

Radius of the pencil (R) = 6mm = 610 cm

Radius of the lead  = r = 3 mm = 310 cm

To find :  Volume of the wood used in the pencil

Solution : Volume of Hollow cylinder = πh(R + r)(R - r)

Volume of the wood in the pencil

= 227 x 29 x (  610 + 310 ) x ( 610 - 310 )

 =  91.14 x ( 910 ) x ( 310 ) cm3

= 91.14X27 / 100 cm3  =  2460.78 / 100  = 24.61 cm3

Volume of the wood used in the pencil is  24.61 cm3