446. A copper rod of 1 cm diameter and 8 cm length is drawn into a wire of uniform diameter and 18 m length. The radius (in cm) of the wire is
     

1. 1. 1/15
      

   
   
   

   2. 1/30
      

   
   
   

   3. 2/15
      

   
   
   

   4. 15

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the radius of wire = r cm.
   

   Volume of copper rod = π ×		1		²	× 8 = 2πcm³
   		2

   
   Volume of wire = πr² × 1800
   = 1800 πr² cm³
   Clearly,
   1800 πr² = 2π
   

   ⇒ r² =	1	⇒ r =	1
   	900		3

   Correct Option: B

   Let the radius of wire = r cm.
   

   Volume of copper rod = π ×		1		²	× 8 = 2πcm³
   		2

   
   Volume of wire = πr² × 1800
   = 1800 πr² cm³
   Clearly,
   1800 πr² = 2π
   

   ⇒ r² =	1	⇒ r =	1
   	900		3

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447. The base of a triangle is increased by 10%. To keep the area unchanged the height of the triangle is to be decreased by
     

1. 1. 9	1	%
      	11

   
   
   

   2. 11	1	%
      	9

   
   
   

   3. 11%
      

   
   
   

   4. 9%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 10, Percentage increase
   

   =		x + y +	x × y		%
   			100

   
   

   ⇒ 0 =		10 + y +	10 y		%
   			100

   
   

   ⇒ - 10 = y +	y
   	10

   
   

   ⇒ - 10 =	10y + y
   	10

   
   ⇒ 11y = – 100
   

   ⇒ y =	- 100	= - 9	1	%
   	11		11

   
   Negative sign shows decrease.
   OR
   
   

   Percentage decrease =	10	× 100
   	100 + 10

   
   

   =	100	= 9	1	%
   	11		11

   Correct Option: A

   Using Rule 10, Percentage increase
   

   =		x + y +	x × y		%
   			100

   
   

   ⇒ 0 =		10 + y +	10 y		%
   			100

   
   

   ⇒ - 10 = y +	y
   	10

   
   

   ⇒ - 10 =	10y + y
   	10

   
   ⇒ 11y = – 100
   

   ⇒ y =	- 100	= - 9	1	%
   	11		11

   
   Negative sign shows decrease.
   OR
   
   

   Percentage decrease =	10	× 100
   	100 + 10

   
   

   =	100	= 9	1	%
   	11		11

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448. If the radius of a cylinder is decreased by 50 % and the height is increased by 50 %, then the change in volume is
     

1. 1. 52.5 %
      

   
   
   

   2. 67.5 %
      

   
   
   

   3. 57.5 %
      

   
   
   

   4. 62.5 %

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 10,
   Single equivalent decrease for 50% and 50%
   

   =		50 - 50 +	50 × 50		% = ( - 100 + 25) % = - 75%
   			100

   
   Single equivalent percent for – 75% and 50%
   

   =		- 75 + 50 -	75 × 50		% = ( - 25 - 37.5) % = - 62.5%
   			100

   
   Negative sign shows decrease.

   Correct Option: D

   Using Rule 10,
   Single equivalent decrease for 50% and 50%
   

   =		50 - 50 +	50 × 50		% = ( - 100 + 25) % = - 75%
   			100

   
   Single equivalent percent for – 75% and 50%
   

   =		- 75 + 50 -	75 × 50		% = ( - 25 - 37.5) % = - 62.5%
   			100

   
   Negative sign shows decrease.

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449. The radius of the base of a Conical tent is 12 m. The tent is 9 m high. Find the cost of canvas required to make the tent, if one square metre of canvas costs 120 (Take π = 3.14 )
     

1. 1. ₹ 67, 830
      

   
   
   

   2. ₹ 67, 800
      

   
   
   

   3. ₹ 67, 820
      

   
   
   

   4. ₹ 67, 824

   
   
   

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1. View Hint View Answer Discuss in Forum

   Slant height of the tent (l) = √12² + 9² = 1√144 + 81
   = √225 = 15 metre
   ∴ Curved surface area of the tent = πrl = (3.14 × 12 × 15) sq. metre
   ∴ Total cost = (3.14 × 12 × 15 × 120) = 67824

   Correct Option: D

   Slant height of the tent (l) = √12² + 9² = 1√144 + 81
   = √225 = 15 metre
   ∴ Curved surface area of the tent = πrl = (3.14 × 12 × 15) sq. metre
   ∴ Total cost = (3.14 × 12 × 15 × 120) = 67824

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450. A metallic sphere of radius 10.5 cm is melted and then recast into small cones each of radius 3.5 cm and height 3 cm. The number of cones thus formed is
     

1. 1. 140
      

   
   
   

   2. 132
      

   
   
   

   3. 112
      

   
   
   

   4. 126

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of sphere =	4	π (10.5)³ cu.cm.
   	3

   
   

   Volume of cone =	1	π (3.5)³ × 3 cu.cm.
   	3

   
   

   ∴ Number of cones =	4	π × (10.5)³	= 126
   	3
   	1	π × (3.5)² × 3
   	3

   Correct Option: D

   Volume of sphere =	4	π (10.5)³ cu.cm.
   	3

   
   

   Volume of cone =	1	π (3.5)³ × 3 cu.cm.
   	3

   
   

   ∴ Number of cones =	4	π × (10.5)³	= 126
   	3
   	1	π × (3.5)² × 3
   	3

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