181. The surface area of a sphere is 64π cm2. Its diameter is equal to
     

1. 1. 16 cm
      

   
   
   

   2. 8 cm
      

   
   
   

   3. 4 cm
      

   
   
   

   4. 2 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   4πr² = 64π sq.cm.
   ⇒ r² = 16
   ⇒ r = 4 cm
   ∴ Diameter = 8 cm

   Correct Option: B

   4πr² = 64π sq.cm.
   ⇒ r² = 16
   ⇒ r = 4 cm
   ∴ Diameter = 8 cm

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182. The diameter of two hollow spheres made from the same metal sheet are 21 cm and 17.5 cm respectively. The ratio of the area of metal sheets required for making the two spheres is
     

1. 1. 6 : 5
      

   
   
   

   2. 36 : 25
      

   
   
   

   3. 3 : 2
      

   
   
   

   4. 18 : 25

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let r1 =	21	cm. and
   	2

   
   

   r2 =	17.5	cm.
   	2

   
   

   ∴ Required ratio =	4πr1²	=	r1²
   	4πr2²		r2²

   
   

   ⇒		21		²
   		2			=		21 × 21	= 36 : 25
   		17.5		²			17.5 × 17.5
   		2

   Correct Option: B

   Let r1 =	21	cm. and
   	2

   
   

   r2 =	17.5	cm.
   	2

   
   

   ∴ Required ratio =	4πr1²	=	r1²
   	4πr2²		r2²

   
   

   ⇒		21		²
   		2			=		21 × 21	= 36 : 25
   		17.5		²			17.5 × 17.5
   		2

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183. When the circumference of a toy ballon is increased from 20 cm to 25 cm, its radius (in cm) is increased by :
     

1. 1. 5
      

   
   
   

   2. 5/π
      

   
   
   

   3. 5/2π
      

   
   
   

   4. π/5

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here, we can treat the balloon as sphere.
   Its circumference = 2πr
   ∴ 2πr₁ = 20 ...(i)
   2πr₂ = 25 ....(ii)
   On dividing equation (ii) by (i),
   

   ⇒	2πr2	=	25	⇒	r2	=	5
   	2πr1		20		r1		4

   
   ∴ Increase = r₂ – r₁
   

   =	5	r1 - r1	1	r1
   	4		4

   
   

   =	1	×	20	=	5	[From(i)
   	4		2π		2π

   Correct Option: C

   Here, we can treat the balloon as sphere.
   Its circumference = 2πr
   ∴ 2πr₁ = 20 ...(i)
   2πr₂ = 25 ....(ii)
   On dividing equation (ii) by (i),
   

   ⇒	2πr2	=	25	⇒	r2	=	5
   	2πr1		20		r1		4

   
   ∴ Increase = r₂ – r₁
   

   =	5	r1 - r1	1	r1
   	4		4

   
   

   =	1	×	20	=	5	[From(i)
   	4		2π		2π

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184. If the volume of two cubes are in the ratio 27 : 64, then the ratio of their total surface area is :
     

1. 1. 27 : 64
      

   
   
   

   2. 3 : 4
      

   
   
   

   3. 9 : 16
      

   
   
   

   4. 3 : 8

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the side of the two cubes are x and y.
   According to the question
   

   	x³	=	27	=	(3)³	, ∴	x	=	3
   	y³		64		(4)³		y		4

   
   We know that surface area of the cube = 6 × (side)²
   ∴ Ratio of their surface areas
   

   =	6x²	=	6 × 3²	=	9	= 9 : 16
   	6y²		6 × 4²		16

   Correct Option: C

   Let the side of the two cubes are x and y.
   According to the question
   

   	x³	=	27	=	(3)³	, ∴	x	=	3
   	y³		64		(4)³		y		4

   
   We know that surface area of the cube = 6 × (side)²
   ∴ Ratio of their surface areas
   

   =	6x²	=	6 × 3²	=	9	= 9 : 16
   	6y²		6 × 4²		16

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185. If the height of a cylinder is increased by 15 per cent and the radius of its base is decreased by 10 per cent then by what percent will its curved surface area change?
     

1. 1. 3.5 per cent decrease
      

   
   
   

   2. 3.5 per cent increase
      

   
   
   

   3. 5 per cent increase
      

   
   
   

   4. 5 per cent decrease

   
   
   

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1. View Hint View Answer Discuss in Forum

   Per cent change in surface area
   

   =		x + y +	xy
   			100

   
   

   =		15 + (-10) +	15 × (-10)
   			100

   
   

   =		15 - 10 -	150		= [15 - 11.5]
   			100

   
   = 3.5 per cent.
   (+ve) sign shows 3.5 per cent increases.

   Correct Option: B

   Per cent change in surface area
   

   =		x + y +	xy
   			100

   
   

   =		15 + (-10) +	15 × (-10)
   			100

   
   

   =		15 - 10 -	150		= [15 - 11.5]
   			100

   
   = 3.5 per cent.
   (+ve) sign shows 3.5 per cent increases.

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