Question

5) If the height of a cylinder triples and its radius becomes one-third, how does the lateral surface area of the cylinder change?
option 1 : it becomes one- third
option 2: it becomes triple
option 3: it remains the same
option 4: it will increase by 3​

Answer 1

Given:-

• The height of cylinder triples
• Radius becomes one-third

To find:-

• How does the lateral surface area of the cylinder change.

Solution:-

Let radius and height of the original cylinder be r and h respectively.

We know,

• Lateral Surface Area of a cylinder = 2πrh sq.units.

Hence,

LSA of original cylinder = 2π × r × h

⇒ LSA of original cylinder = 2πrh ⟶ (i)

For new cylinder,

• radius becomes one-third
• height triples

Therefore,

• radius = 1/3r
• height = 3h

Hence,

LSA of new cylinder = 2π × 1/3r × 3h

⇒ LSA of new cylinder = 2πrh ⟶ (ii)

From (i) and(ii) we can see that there is no change in LSA even if the radius is reduced to one-third and height is tripled.

From here we can conclude:-

The Lateral surface area remains the same.

Hence [option 3: it remains the same] is the correct answer.

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Some other formulas related to cylinder:-

• Volume = πr²h cu.units
• TSA = 2πr(r + h) sq.units

Note:- TSA here denotes Total Surface Area.

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Answer 2

Answer:

$\huge{\bf{\underline{\red{Given:}}}}$

$\rightarrow$Volume of πr²h

Now,

r = $\large{\frac{r}{2}\&h = h2}$

New CSA = $\boxed{\red{2πrh}}$

$\large= 2\pi (\frac{r}{2} ) \times (h \times 2)$

$\rightarrow$$\boxed{\orange{2πrh}}$

$\huge{ \mathfrak{ \underline{Answer}}}$

Option 3: It will remain Same