146. The volume of a right rectangular pyramid is 220 m3. What is the height of the pyramid, if the area of its base is 55 m² ?
     

1. 1. 8 metre
      

   
   
   

   2. 13.5 metre
      

   
   
   

   3. 12 metre
      

   
   
   

   4. 9 metre

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of pyramid =	1	× area of base × height
   	3

   
   

   ⇒ 220 =	1	× 55 × height
   	3

   
   

   ⇒ Height =	220 × 3	= 12 metre
   	55

   Correct Option: C

   Volume of pyramid =	1	× area of base × height
   	3

   
   

   ⇒ 220 =	1	× 55 × height
   	3

   
   

   ⇒ Height =	220 × 3	= 12 metre
   	55

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147. The radius of a wire is decreased to one third. If volume remains the same, length will increase by:
     

1. 1. 6 times
      

   
   
   

   2. 1 time
      

   
   
   

   3. 3 times
      

   
   
   

   4. 9 times

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of wire = πr²h
   

   when r1 =	r	, h1 = ?
   	3

   
   ∴ πr²h = πr₁²h₁
   

   ⇒ r²h =		r		²	× h1
   		3

   
   ⇒ h₁ = 9h

   Correct Option: D

   Volume of wire = πr²h
   

   when r1 =	r	, h1 = ?
   	3

   
   ∴ πr²h = πr₁²h₁
   

   ⇒ r²h =		r		²	× h1
   		3

   
   ⇒ h₁ = 9h

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148. A prism with a right triangular base is 25 cm high. If the shorter sides of the triangle are in the ratio of 1 : 2 and the volume of the prism is 100 cm³, what is the length of the longest side of the triangle?
     

1. 1. √5cm
      

   
   
   

   2. 2√5cm
      

   
   
   

   3. 5√2cm
      

   
   
   

   4. 5 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of prism = Area of base × height
   

   ⇒ 100 =	1	× x × 2x × 25
   	2

   
   

   ⇒ x² =	100	= 4
   	25

   
   ⇒ x = 2
   ∴ Smaller sides of triangle = 2 cm and 4 cm
   ∴ Largest side = √2² + 4²
   = √4 + 16 = √20
   = 2√5 cm.
   [∵ The triangle is right angled.]

   Correct Option: B

   Volume of prism = Area of base × height
   

   ⇒ 100 =	1	× x × 2x × 25
   	2

   
   

   ⇒ x² =	100	= 4
   	25

   
   ⇒ x = 2
   ∴ Smaller sides of triangle = 2 cm and 4 cm
   ∴ Largest side = √2² + 4²
   = √4 + 16 = √20
   = 2√5 cm.
   [∵ The triangle is right angled.]

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149. The ratio of the volume of a cube to that of a sphere which will fit inside the cube is
     

1. 1. 4 : π
      

   
   
   

   2. 4 : 3π
      

   
   
   

   3. 6 : π
      

   
   
   

   4. 2 : π

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the edge of cube be a units.
   Its volume = a³ cubic units
   

   Radius of sphere =	a	units
   	2

   
   

   	4	units
   	2

   
   

   Volume of sphere =	4	π		a		³	=	πa³	cubic unit
   	3			2				6

   
   

   ∴ Required ratio = a³ :	πa³	= 6 : π
   	6

   Correct Option: C

   Let the edge of cube be a units.
   Its volume = a³ cubic units
   

   Radius of sphere =	a	units
   	2

   
   

   	4	units
   	2

   
   

   Volume of sphere =	4	π		a		³	=	πa³	cubic unit
   	3			2				6

   
   

   ∴ Required ratio = a³ :	πa³	= 6 : π
   	6

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150. The height of a right circular cylinder is three times the radius of the base. If the height were four times the radius, the volume would be 1078 cubic centimetre more than it was previously. Find the radius of the base.
     

1. 1. 6 cm
      

   
   
   

   2. 5 cm
      

   
   
   

   3. 7.5 cm
      

   
   
   

   4. 7 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the radius of base = r cm
   ∴ h₁ = 3r cm.
   h₂ = 4r cm.
   According to the question,
   πr²h₂ - πr²h₁ = 1078
   ⇒ πr² (h₂ - h₁) = 1078
   

   ⇒	22	r²(4r - 3r) = 1078
   	7

   
   

   ⇒	22	r³ = 1078
   	7

   
   

   ⇒ r³ =	1078 × 7	= 49 × 7
   	22

   
   ∴ r = ³√49 × 7 = 7 cm.

   Correct Option: D

   Let the radius of base = r cm
   ∴ h₁ = 3r cm.
   h₂ = 4r cm.
   According to the question,
   πr²h₂ - πr²h₁ = 1078
   ⇒ πr² (h₂ - h₁) = 1078
   

   ⇒	22	r²(4r - 3r) = 1078
   	7

   
   

   ⇒	22	r³ = 1078
   	7

   
   

   ⇒ r³ =	1078 × 7	= 49 × 7
   	22

   
   ∴ r = ³√49 × 7 = 7 cm.

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