Question

If base radius and height of a cylinder are increased by 100% then its volume increased by:

(a) 30% (b) 40% (c) 42% (d) 33.1%
pls answer correctly​

Answer 1

Answer:

If radius is increased by 100% then the new radius will be 2r because 100% of r = r only so similarly the new height also becomes 2h

V=πr²h....... formula for volume of cylinder

v=π(2r)²2h........ substitute new values

v=π(4r²)2h

v=8πr²h

v=8(πr²h)

Here πr²h is the old volume when no value is increased

Therefore the volume of the cylinder increase by a factor of 8 when the radius and height are increased by 100%.

Then after converting into percentage we get 33.1

Then the volume increases by 33.1%

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Answer 2

Given: Base radius and height of cylinder is increased by 100%.

To find: Percentage change in volume

Solution: Let the radius and height be r and h respectively.

When radius is increased by 100%, new radius

= Original radius + 100% of orginal radius

= r + (100/100) × r

= r + r

= 2r

When height is increased by 100%, new height

= Original height + 100% of orginal height

= h + (100/100) × h

= h + h

= 2h

Volume of original cylinder is

$= \pi {r}^{2} h$

Volume of new cylinder is

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

$= 8\pi {r}^{2} h$

Increase in volume

= New volume- Original volume

$8\pi {r}^{2} h - \pi {r}^{2} h$

$= 7\pi {r}^{2} h$

Percentage change in volume

= (Change in volume/Original volume) × 100

$= \frac{7\pi {r}^{2} \times h }{\pi {r}^{2} \times h } \times 100$

= 7 × 100

= 700%

Here, none of the options matches the answer to the question.

Therefore, the volume of the cylinder increases by 700% on increasing the base radius and cylinder by 100%.