Question

the radii of two cylinder are in the ratio 3:2 and Heights in the ratio 4:2. The ratio of their volumes is​



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Answer 1

Answer:

36:8

Step-by-step explanation:

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Answer 2

$\huge\mathbb{SOLUTION:-}$

$\bold{Given:-}\begin{cases}\sf{Radii \:if\: cylinders\:in\: ratio=3:2}\\ \sf{Height\:in\: ratio=4:2}\end{cases}$

• We have to find the ratio of their volumes

$\boxed{\sf{Volume\:of\: cylinder=\pi r{}^{2}h}}$

• We have to find the ratio of volumes of two cylinder

• Let the radius of first cylinder be 3r

• and height be 4h

• Now volume :-

$\sf\implies Volume\:of\: cylinder_1=\pi(3r){}^{2}\times 4h\\ \\ \sf\implies Volume\:of\: cylinder_1=\pi 9r{}^{2}\times 4h\\ \\ \sf\implies volume\:of\: cylinder_1=9r{}^{2}\pi 4h$

$\boxed{\sf{\red{Volume\:of\: cylinder_1= 9r{}^{2} \pi 4h}}}$

• Now the volume of 2nd cylinder
• it's radius be 2r and height be 2h

$\sf\implies Volume\:of\:cylinder_2=\pi(2r){}^{2}\times 2h\\ \\ \sf\implies Volume\:of\: cylinder_2= \pi 4r{}^{2}\times 2h\\ \\ \sf\implies Volume\:of\: cylinder_2= \pi 4r{}^{2} 2h$

$\boxed{\sf{\red{Volume\:of\: cylinder_2=\pi 4r{}^{2} 2h}}}$

• NOW THE RATIO OF THEIR VOLUME

$\boxed{\sf{Ratio=\frac{Volume\:of\: cylinder_1}{Volume\:of\: cylinder_2}}}$

$\sf\implies ratio=\frac{9\cancel{r{}^{2}}\cancel{\pi} \cancel{4h}}{4\cancel{r{}^{2}}\cancel{\pi} \cancel{2h}}\\ \\ \sf\implies Ratio= \frac{9\times 2}{4}\\ \\ \sf\implies Ratio=\cancel{\frac{18}{4}}\\ \\ \sf\implies Ratio=\frac{9}{2}\\ \\ \sf\implies ratio=9:2$

$\boxed{\sf{\purple{Ratio\:of\:their\:volumes=9:2}}}$

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