391. The sum of radii of two spheres is 10 cm and the sum of their volume is 880 cm3. What will be the product of their radii ?
     

1. 1. 21
      

   
   
   

   2. 26	1
      	3

   
   
   

   3. 33	1
      	3

      
      

   
   
   

   4. 70

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to question r₁ + r₂ = 10 ... (i)
   

   ⇒	4	π (r1³ + r2³) = 880
   	3

   
   

   ⇒ r1³ + r2³ =	880 × 3 × 7	= 210......(ii)
   	22 × 4

   \ (r1+ r2)3 = 1000 Þr13+ r23 + 3r1r2 (r1+ r2) = 1000 Þ210 + 3r1r2 (10) = 1000 Þ30r1r2 = 1000 – 210 = 790
   ⇒ (r₁ + r₂)³ = 1000
   ⇒ r₁³ + r₂³ + 3r₁r₂(r₁ + r₂) = 1000
   210 + 3r₁r₂ (10) = 1000
   

   ⇒ r1r2 =	790	=	79	= 26	1
   	30		3		3

   Correct Option: B

   According to question r₁ + r₂ = 10 ... (i)
   

   ⇒	4	π (r1³ + r2³) = 880
   	3

   
   

   ⇒ r1³ + r2³ =	880 × 3 × 7	= 210......(ii)
   	22 × 4

   \ (r1+ r2)3 = 1000 Þr13+ r23 + 3r1r2 (r1+ r2) = 1000 Þ210 + 3r1r2 (10) = 1000 Þ30r1r2 = 1000 – 210 = 790
   ⇒ (r₁ + r₂)³ = 1000
   ⇒ r₁³ + r₂³ + 3r₁r₂(r₁ + r₂) = 1000
   210 + 3r₁r₂ (10) = 1000
   

   ⇒ r1r2 =	790	=	79	= 26	1
   	30		3		3

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392. If the radius of a sphere is doubled, its volume becomes
     

1. 1. double
      

   
   
   

   2. four times
      

   
   
   

   3. six times
      

   
   
   

   4. eight times

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of sphere =	4	πr³
   	3

   
   

   Volume of second sphere =	4	π(2r)³ = 8 ×		4	πr³
   	3			3

   Correct Option: D

   Volume of sphere =	4	πr³
   	3

   
   

   Volume of second sphere =	4	π(2r)³ = 8 ×		4	πr³
   	3			3

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393. The radii of two spheres are in the ratio 3 : 2. Their volume will be in the ratio :
     

1. 1. 9 : 4
      

   
   
   

   2. 3 : 2
      

   
   
   

   3. 8 : 27
      

   
   
   

   4. 27 : 8

   
   
   

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1. View Hint View Answer Discuss in Forum

   Ratio of the volume of both spheres =	4	πr1³
   	3		=		r1		³	=		3		³	×	27	or 27 : 8
   	4	πr³			r2					2				8
   	3

   Correct Option: D

   Ratio of the volume of both spheres =	4	πr1³
   	3		=		r1		³	=		3		³	×	27	or 27 : 8
   	4	πr³			r2					2				8
   	3

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394. The total surface area of a solid hemisphere is 108π cm². The volume of the hemisphere is
     

1. 1. 72π cm³
      

   
   
   

   2. 144π cm³
      

   
   
   

   3. 108√6 cm³
      

   
   
   

   4. 54√6 cm³

   
   
   

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1. View Hint View Answer Discuss in Forum

   If the radius of the solid hemisphere be r cm,
   then total surface area = 3πr²
   ⇒ 3πr² = 108π
   

   ⇒ r² =	108	= 36
   	3

   
   ⇒ r = √36 = 6 cm
   

   ∴ Volume of the hemisphere =	2	πr³
   	3

   
   

   ∴ Volume of the hemisphere =	2	π × 6 × 6 × 6 = 144π cubic cm.
   	3

   Correct Option: B

   If the radius of the solid hemisphere be r cm,
   then total surface area = 3πr²
   ⇒ 3πr² = 108π
   

   ⇒ r² =	108	= 36
   	3

   
   ⇒ r = √36 = 6 cm
   

   ∴ Volume of the hemisphere =	2	πr³
   	3

   
   

   ∴ Volume of the hemisphere =	2	π × 6 × 6 × 6 = 144π cubic cm.
   	3

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395. The largest sphere is carved out of a cube of side 7 cm. The volume of the sphere (in cm³) will be
     

1. 1. 718.66
      

   
   
   

   2. 543.72
      

   
   
   

   3. 481.34
      

   
   
   

   4. 179.67

   
   
   

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1. View Hint View Answer Discuss in Forum

   Radius of the largest sphere =	7	cm
   	2

   
   

   ∴ Volume of sphere =	4	πr³
   	3

   
   

   =		4	×	22	×	7	×	7	×	7	×		cm³.
   		3		7		2		2		2

   
   = 179.67 cm³

   Correct Option: D

   Radius of the largest sphere =	7	cm
   	2

   
   

   ∴ Volume of sphere =	4	πr³
   	3

   
   

   =		4	×	22	×	7	×	7	×	7	×		cm³.
   		3		7		2		2		2

   
   = 179.67 cm³

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