406. If the base of a right pyramid is triangle of sides 5 cm, 12 cm, 13 cm and its volume is 330 cm³, then its height (in cm) will be
     

1. 1. 33
      

   
   
   

   2. 32
      

   
   
   

   3. 11
      

   
   
   

   4. 22

   
   
   

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1. View Hint View Answer Discuss in Forum

   Area of base = Area of right angled triangle =	1	× 5 × 12 = 30 sq.cm.
   	2

   
   [∵ 5² + 12² = 13²]
   

   ∴ Volume =	1	× Area of base × height
   	3

   
   

   ⇒ 330 =	1	× 30 × h
   	3

   
   

   ⇒ 330 =	330	× 33 cm./td>
   	10

   Correct Option: A

   Area of base = Area of right angled triangle =	1	× 5 × 12 = 30 sq.cm.
   	2

   
   [∵ 5² + 12² = 13²]
   

   ∴ Volume =	1	× Area of base × height
   	3

   
   

   ⇒ 330 =	1	× 30 × h
   	3

   
   

   ⇒ 330 =	330	× 33 cm./td>
   	10

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407. The diameter of the moon is assumed to be one fourth of the diameter of the earth. Then the ratio of the volume of the earth to that of the moon is
     

1. 1. 64 : 1
      

   
   
   

   2. 1 : 64
      

   
   
   

   3. 60 : 7
      

   
   
   

   4. 7 : 60

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of earth : Volume of moon =	4	πr³ =	4	π ×		r		²	= 64 : 1
   	3		3			4

   Correct Option: A

   Volume of earth : Volume of moon =	4	πr³ =	4	π ×		r		²	= 64 : 1
   	3		3			4

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408. A solid metallic sphere of radius 3 decimetres is melted to form a circular sheet of 1 milimetre thickness. The diameter of the sheet so formed is
     

1. 1. 26 metres
      

   
   
   

   2. 24 metres
      

   
   
   

   3. 12 metres
      

   
   
   

   4. 6 metres

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of solid sphere =	4	πr³
   	3

   
   

   Volume of solid sphere =	4	π(0.3)³ cubic metre
   	3

   
   If the radius of the circular sheet be R, then
   Volume of the sheet = πR² × 0.001
   

   Volume of solid sphere =	4	π(0.3)³
   	3

   
   

   R² × 0.001 =	4	× 0.3 × 0.3 × 0.3
   	3

   
   R² = 36 ⇒ R = 6 metres
   ∴ Diameter = 12 metres

   Correct Option: C

   Volume of solid sphere =	4	πr³
   	3

   
   

   Volume of solid sphere =	4	π(0.3)³ cubic metre
   	3

   
   If the radius of the circular sheet be R, then
   Volume of the sheet = πR² × 0.001
   

   Volume of solid sphere =	4	π(0.3)³
   	3

   
   

   R² × 0.001 =	4	× 0.3 × 0.3 × 0.3
   	3

   
   R² = 36 ⇒ R = 6 metres
   ∴ Diameter = 12 metres

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409. Two solid cylinders of radii 4 cm and 5cm and length 6 cm and 4 cm respectively are recast into cylindrical disc of thickness 1 cm. The radius of the disc is
     

1. 1. 7 cm
      

   
   
   

   2. 14 cm
      

   
   
   

   3. 21 cm
      

   
   
   

   4. 28 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Sum of the volume of two cylinders = πr₁²h₁ + πr₂²h₂
   

   =	22	(4 × 4 × 6 + 5 × 5 × 4)
   	7

   
   

   =	22	(96 + 100)
   	7

   
   

   =	22	× 196 = 616 cm³
   	7

   
   Let the radius of the disc be r cm.
   ∴ πr² × 1 = 616
   

   ⇒ r² =	22	× r² = 616
   	7

   
   

   ⇒ r² =	616 × 7	= 196
   	22

   
   ⇒ r = √196 = 14 cm

   Correct Option: B

   Sum of the volume of two cylinders = πr₁²h₁ + πr₂²h₂
   

   =	22	(4 × 4 × 6 + 5 × 5 × 4)
   	7

   
   

   =	22	(96 + 100)
   	7

   
   

   =	22	× 196 = 616 cm³
   	7

   
   Let the radius of the disc be r cm.
   ∴ πr² × 1 = 616
   

   ⇒ r² =	22	× r² = 616
   	7

   
   

   ⇒ r² =	616 × 7	= 196
   	22

   
   ⇒ r = √196 = 14 cm

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410. Two solid cylinders of radii 4 cm and 5cm and length 6 cm and 4 cm respectively are recast into cylindrical disc of thickness 1 cm. The radius of the disc is
     

1. 1. 7 cm
      

   
   
   

   2. 14 cm
      

   
   
   

   3. 21 cm
      

   
   
   

   4. 28 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Sum of the volume of two cylinders = πr₁²h₁ + πr₂²h₂
   

   =	22	(4 × 4 × 6 + 5 × 5 × 4)
   	7

   
   

   =	22	(96 + 100)
   	7

   
   

   =	22	× 196 = 616 cm³
   	7

   
   Let the radius of the disc be r cm.
   ∴ πr² × 1 = 616
   

   ⇒ r² =	22	× r² = 616
   	7

   
   

   ⇒ r² =	616 × 7	= 196
   	22

   
   ⇒ r = √196 = 14 cm

   Correct Option: B

   Sum of the volume of two cylinders = πr₁²h₁ + πr₂²h₂
   

   =	22	(4 × 4 × 6 + 5 × 5 × 4)
   	7

   
   

   =	22	(96 + 100)
   	7

   
   

   =	22	× 196 = 616 cm³
   	7

   
   Let the radius of the disc be r cm.
   ∴ πr² × 1 = 616
   

   ⇒ r² =	22	× r² = 616
   	7

   
   

   ⇒ r² =	616 × 7	= 196
   	22

   
   ⇒ r = √196 = 14 cm

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