A right circular hollow cylinder has an outer radius of R and inner radius of r. Which of the following statements hold true if h is the height of the cylinder? (i) Curved surface area of the cylinder = 2\pi(R+r)h

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Solution

Q.
A right circular hollow cylinder has an outer radius of R and inner radius of r. Which of the following statements hold true if h is the height of the cylinder

(i) Curved surface area of the cylinder $= 2 π (R + r) h$

(ii) Total surface area of the cylinder $= 2 π (R + r) (R + h - r)$

(iii) Total volume of the cylinder $= π (R^{2} - r^{2}) h$

(iv) Total volume of the cylinder $= π (R^{2} + r^{2}) h$

Choose the correct option from the following:

1 Only (iv)

2 (i) and (iii)

3 (i), (ii) and (iii)

4 (i), (ii) and (iv)

Ans.
(3)

Curved surface area = External curved surface area + Internal curved surface area

$= 2 π R h + 2 π r h = 2 π (R + r) h$

$(ii) Total surface area = 2 π R h + 2 π r h + 2 (π R^{2} - π r^{2})$

$= 2 π (R + r) h + 2 π (R + r) (R - r)$

$= 2 π (R + r) (R + h - r)$

$(iii) Total volume = π R^{2} h - π r^{2} h = π h (R^{2} - r^{2})$

$∴ Option (c) is correct.$

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