Question

please solve this question​

Answer 1

Step-by-step explanation:

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

Thus,

Original volume of cylinder $=\pi r^2 h.....(1)$

On increasing the radius by 20%.

New radius

$=r+20\% \: of \:r\\</p><p>r+0.2r\\</p><p>=1.2r$

On decreasing the height by 20%.

New height

$=h-20\% \: of \:h\\</p><p>=h-0.2h\\</p><p>=0.8h$

New volume of cylinder

$=\pi (1.2r)^2 \times 0.8h\\=\pi \times 1.44r^2 \times 0.8h\\</p><p>=1.152\pi r^2 h.....(2)$

Change in volume $=1.152\pi r^2h-\pi r^2h\\=0.152\pi r^2h\\</p><p>Percentage\:change\:in \:volume \\= \frac {0.152\pi r^2h}{\pi r^2h}\times 100\\=0.152\times 100\\</p><p>=15.2\%$