Question 7

If the height of a cylinder becomes $\frac{1}{4}$ of the original height and the radius is doubled, then which of the following will be true ?
(a) Total surface area of the cylinder will be doubled
(b) Total surface area of the cylinder will remain unchanged
(c) Total surface area of the cylinder will be halved
(d) None of the above

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Solution

We know that,
Total surface area of cylinder having radius r and height $h = 2 π r (h + r)$
Total surface area of the cylinder with new height $(\frac{h}{4})$ and radius 2r
$= 2 π (2 r) (2 r + \frac{1}{4} h)$
$= 4 π r (8 r + h) \times \frac{1}{4}$
$= π r (8 r + h)$

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Question 6

If the height of a cylinder becomes $\frac{1}{4}$ of the original height and the radius is doubled, then which of the following will be true ?
(a) Curved surface area of the cylinder will be doubled
(b) Curved surface area of the cylinder will remain unchanged
(c) Curved surface area of the cylinder will be halved
(d) Curved surface area will be $\frac{1}{4}$ of the original curved surface

Question 5

If the height of a cylinder becomes $\frac{1}{4}$ of the original height and the radius is doubled, then which of the following will be true ?
(a) Volume of the cylinder will be doubled
(b) Volume of the cylinder will remain unchanged
(c) Volume of the cylinder will be halved
(d) Volume of the cylinder will be $\frac{1}{4}$ of the original volume

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The height of a circular cylinder is 2 cm and radius of its base is 7 cm. Then, the total surface area of the cylinder will be (in centimetre square) ___

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Standard X Mathematics

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We know that, Total surface area of cylinder having radius r and height h=2πr(h+r) Total surface area of the cylinder with new height (h4) and radius 2r =2π(2r)(2r+14h) =4πr(8r+h)×14 =πr(8r+h)

We know that,
Total surface area of cylinder having radius r and height $h = 2 π r (h + r)$
Total surface area of the cylinder with new height $(\frac{h}{4})$ and radius 2r
$= 2 π (2 r) (2 r + \frac{1}{4} h)$
$= 4 π r (8 r + h) \times \frac{1}{4}$
$= π r (8 r + h)$