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Right Circular Cylinder

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Right Circular Cylinder

Right Circular Cylinder
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Multiple Choice Questions (MCQ)

  1. What is the formula for the curved surface area (CSA) of a right circular cylinder?
     A. πr²h
     B. 2πrh
     C. 2πr(h + r)
     D. πrh²
     Answer: B. 2πrh
  2. If the radius of a cylinder is 3 cm and the height is 7 cm, what is its volume?
     A. 198 cm³
     B. 132 cm³
     C. 154 cm³
     D. 66 cm³
     Answer: A. 198 cm³
     (V = πr²h = 22/7 × 3² × 7 = 198 cm³)
  3. The total surface area (TSA) of a cylinder includes:
     A. Only one circular base and side surface
     B. Two circular bases only
     C. Side surface and both circular bases
     D. Only the side surface
     Answer: C. Side surface and both circular bases
  4. Which of the following is not a real-life example of a right circular cylinder?
     A. Water tank
     B. Tin can
     C. Cubical box
     D. Pipe
     Answer: C. Cubical box
  5. If CSA = 440 cm² and height = 10 cm, then what is the radius of the cylinder?
     A. 7 cm
     B. 6 cm
     C. 5 cm
     D. 8 cm
     Answer: A. 7 cm
     (CSA = 2πrh ⇒ 440 = 2 × 22/7 × r × 10 ⇒ r = 7)

Short Answer Questions (SAQ)

  1. Write the formula for the volume of a right circular cylinder.
     Answer: Volume = πr²h
  2. A cylinder has a height of 14 cm and radius of 7 cm. What is its total surface area (TSA)?
     Answer: Total surface area  = 2πr(h + r)
     = 2 × 22/7 × 7 × (14 + 7) = 924 cm²
  3. Mention one difference between curved surface area (CSA) and total surface area (TSA).
     Answer: Curved surface area includes only the lateral/side surface, while total surface area  includes curved surface area plus both circular bases.

Long Answer Questions (LAQ)

1.A cylindrical tank has radius 5 cm and height 10 cm.
(a) Find the curved surface area (CSA)
(b) Find the total surface area (TSA)
(c) State which formulae you used

Answer: (a) CSA = 2πrh = 2 × 22/7 × 5 × 10 = 314.29 cm²
 (b) TSA = 2πr(h + r) = 2 × 22/7 × 5 × (10 + 5) = 471.43 cm²
 (c) Used formulae: CSA = 2πrh and TSA = 2πr(h + r)

2.The volume of a right circular cylinder is 616 cm³ and the radius is 4 cm.
(a) Find the height of the cylinder.
(b) Write the formula used.
(c) Give one real-life application of this calculation.

Answer: (a) Volume = πr²h
 ⇒ 616 = 22/7 × 4² × h ⇒ 616 = 22/7 × 16 × h
 ⇒ h = (616 × 7) / (22 × 16) = 12.25 cm
 (b) Formula used: Volume = πr²h
 (c) Real-life use: To calculate the water storage capacity of a tank.

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