536. If the slant height of a right pyramid with square base is 4 metre and the total slant surface of the pyramid is 12 square metre, then the ratio of total slant surface and area of the base is :
     

1. 1. 16 : 3
      

   
   
   

   2. 24 : 5
      

   
   
   

   3. 32 : 9
      

   
   
   

   4. 12 : 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the length of each side of base be x metres, then
   

   	1	× perimeter of base × slant height = 12
   	2

   
   

   ⇒	1	× 4x × 4 = 12
   	2

   
   

   ⇒ x =	12	=	3	metre
   	8		2

   
   

   ∴ Area of the base =	9	sq. metre
   	4

   
   

   ∴ Required ratio = 12 :	9	= 16 : 3
   	4

   Correct Option: A

   Let the length of each side of base be x metres, then
   

   	1	× perimeter of base × slant height = 12
   	2

   
   

   ⇒	1	× 4x × 4 = 12
   	2

   
   

   ⇒ x =	12	=	3	metre
   	8		2

   
   

   ∴ Area of the base =	9	sq. metre
   	4

   
   

   ∴ Required ratio = 12 :	9	= 16 : 3
   	4

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537. The base of a right pyramid is a square of side 16 cm long. If its height be 15 cm, then the area of the lateral surface in square centimetre is :
     

1. 1. 136
      

   
   
   

   2. 544
      

   
   
   

   3. 800
      

   
   
   

   4. 1280

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   Height of the triangle = √15² + 8²
   = √225 + 64 = √283
   = 17 cm
   ∴ Area of the lateral surface of pyramid = 4 × Area of triangle
   

   = 4 ×	1	× base × height
   	2

   
   

   = 4 ×	1	× 16 × 17 = 544 sq.cm.
   	2

   Correct Option: B

   
   Height of the triangle = √15² + 8²
   = √225 + 64 = √283
   = 17 cm
   ∴ Area of the lateral surface of pyramid = 4 × Area of triangle
   

   = 4 ×	1	× base × height
   	2

   
   

   = 4 ×	1	× 16 × 17 = 544 sq.cm.
   	2

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538. The base of a right prism is an equilateral triangle of area 173 cm² and the volume of the prism is 10380 cm³. The area of the lateral surface of the prism is (use √3 = 1.73)
     

1. 1. 1200 cm²
      

   
   
   

   2. 2400 cm²
      

   
   
   

   3. 3600 cm²
      

   
   
   

   4. 4380 cm²

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of right prism = Area of the base × height
   ⇒ 10380 = 173 × h
   

   ⇒ h =	10380	= 60 cm
   	173

   
   Now, Area of triangle
   

   =	√3	× (side)²
   	4

   
   

   ⇒ 173 =	√3	× (side)²
   	4

   
   

   ⇒ 173 =	√3	× (side)²
   	4

   
   ∴ Perimeter = 3 × 20 = 60 cm
   ∴ Area of the lateral surface = Perimeter of base × height = 60 × 60 = 3600 sq.cm.

   Correct Option: C

   Volume of right prism = Area of the base × height
   ⇒ 10380 = 173 × h
   

   ⇒ h =	10380	= 60 cm
   	173

   
   Now, Area of triangle
   

   =	√3	× (side)²
   	4

   
   

   ⇒ 173 =	√3	× (side)²
   	4

   
   

   ⇒ 173 =	√3	× (side)²
   	4

   
   ∴ Perimeter = 3 × 20 = 60 cm
   ∴ Area of the lateral surface = Perimeter of base × height = 60 × 60 = 3600 sq.cm.

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539. The base of a solid right prism is a triangle whose sides are 9 cm, 12 cm and 15 cm. The height of the prism is 5 cm. Then, the total surface area of the prism is
     

1. 1. 180 cm²
      

   
   
   

   2. 234 cm²
      

   
   
   

   3. 288 cm²
      

   
   
   

   4. 270 cm²

   
   
   

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1. View Hint View Answer Discuss in Forum

   Perimeter of triangle
   

   S =	9 + 12 + 15	= 18 cm
   	2

   
   ∴ Area of triangle = √s (s - a)(s - b)(s - c)
   = √18(18 - 9)(18 - 12)(18 - 15)
   = √18 × 9 × 6 × 3 = 54 sq.cm.
   ∴ Total surface area of the prism = Perimeter of base × height + 2 × Area of base
   = 36 × 5 + 2 × 54 = 288 sq.cm.

   Correct Option: C

   Perimeter of triangle
   

   S =	9 + 12 + 15	= 18 cm
   	2

   
   ∴ Area of triangle = √s (s - a)(s - b)(s - c)
   = √18(18 - 9)(18 - 12)(18 - 15)
   = √18 × 9 × 6 × 3 = 54 sq.cm.
   ∴ Total surface area of the prism = Perimeter of base × height + 2 × Area of base
   = 36 × 5 + 2 × 54 = 288 sq.cm.

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540. If the total surface area of a hemisphere is 27π square cm, then the radius of the base of the hemisphere is
     

1. 1. 9√3 cm
      

   
   
   

   2. 3 cm
      

   
   
   

   3. 3√3 cm
      

   
   
   

   4. 9 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   If the radius of hemisphere be r cm,
   then 2πr² + πr² = 27π
   ⇒ 3πr² = 27π
   ⇒ 3r² = 27
   ⇒ r² = 9
   ∴ r = 9 = 3 cm

   Correct Option: B

   If the radius of hemisphere be r cm,
   then 2πr² + πr² = 27π
   ⇒ 3πr² = 27π
   ⇒ 3r² = 27
   ⇒ r² = 9
   ∴ r = 9 = 3 cm

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