796. The radius of the base of a right circular cone is doubled keeping its height fixed. The volume of the cone will be :
     

1. 1. three times of the previous volume
      

   
   
   

   2. four times of the previous volume
      

   
   
   

   3. √2 times of the previous volume

   
   
   

   4. double of the previous volume

   
   
   

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1. View Hint View Answer Discuss in Forum

   Original volume of cone =	1	πr²h
   	3

   
   

   New volume of cone =	1	π(2r)²h =	4	πr²h
   	3		3

   
   

   = 4 ×	1	πr²h
   	3

   
   i.e. Four times of the previous volume.

   Correct Option: B

   Original volume of cone =	1	πr²h
   	3

   
   

   New volume of cone =	1	π(2r)²h =	4	πr²h
   	3		3

   
   

   = 4 ×	1	πr²h
   	3

   
   i.e. Four times of the previous volume.

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797. The heights of two cones are in the ratio 1 : 3 and the diameters of their base are in the ratio 3 : 5. The ratio of their volume is
     

1. 1. 3 : 25
      

   
   
   

   2. 4 : 25
      

   
   
   

   3. 6 : 25
      

   
   
   

   4. 7 : 25

   
   
   

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1. View Hint View Answer Discuss in Forum

   Required ratio =

   1

   πr1²h1

   3

   =

   r1

   ²

   ×

   h1

   =

   3

   ²

   ×

   1

   1

   πr²h

   r2

   h2

   5

   3

   3

   
   

   =	3	⇒ 3 : 25
   	25

   Correct Option: A

   Required ratio =

   1

   πr1²h1

   3

   =

   r1

   ²

   ×

   h1

   =

   3

   ²

   ×

   1

   1

   πr²h

   r2

   h2

   5

   3

   3

   
   

   =	3	⇒ 3 : 25
   	25

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798. The base of a right circular cone has the same radius a as that of a sphere. Both the sphere and the cone have the same volume. Height of the cone is

1. 1. 3a
      

   
   
   

   2. 4a
      

   
   
   

   3. 	7	a
      	4

      
      

   
   
   

   4. 	7	a
      	3

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   	1	πa²h =	4	πa²
   	3		3

   
   ⇒ h = 4a

   Correct Option: B

   
   

   	1	πa²h =	4	πa²
   	3		3

   
   ⇒ h = 4a

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799. The circumference of the base of a 16cm height solid cone is 33cm. What is the volume of the cone in cm³ ?
     

1. 1. 1028
      

   
   
   

   2. 616
      

   
   
   

   3. 462
      

   
   
   

   4. 828

   
   
   

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1. View Hint View Answer Discuss in Forum

   Circumference of the base of cone = 33 cm
   ⇒ 2πr = 33
   

   ⇒ 2 ×	22	× r = 33
   	7

   
   

   ⇒ r =	33 × 7	=	21	cm.
   	2 × 22		4

   
   

   ∴ Volume of the cone =	1	πr²h
   	3

   
   

   =	1	×	22	×	21	×	21	× 16 = 462 cu.cm.
   	3		7		4		4

   Correct Option: C

   Circumference of the base of cone = 33 cm
   ⇒ 2πr = 33
   

   ⇒ 2 ×	22	× r = 33
   	7

   
   

   ⇒ r =	33 × 7	=	21	cm.
   	2 × 22		4

   
   

   ∴ Volume of the cone =	1	πr²h
   	3

   
   

   =	1	×	22	×	21	×	21	× 16 = 462 cu.cm.
   	3		7		4		4

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800. The perimeter of the base of a right circular cone is 8 cm. If the height of the cone is 21 cm, then its volume is:
     

1. 1. 108π cm³
      

   
   
   

   2. 	112	cm³
      	π

      
      

   
   
   

   3. 112π cmsup3;
      

   
   
   

   4. 	108	cm³
      	π

   
   
   

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1. View Hint View Answer Discuss in Forum

   2πr = 8 ⇒ πr = 4
   

   ⇒ r =	4
   	π

   
   

   ∴ V =	1	πr²h -	1	π ×	4 × 4	× 21 =	112	cu.cm.
   	3		3		π × π		π

   Correct Option: B

   2πr = 8 ⇒ πr = 4
   

   ⇒ r =	4
   	π

   
   

   ∴ V =	1	πr²h -	1	π ×	4 × 4	× 21 =	112	cu.cm.
   	3		3		π × π		π

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