Question

JUUM 10 MI. IMU 113 liigill.
4. The radii of two right circular cylinders are in the ratio of 2 : 3 and their heights are in the ratio
of 5 : 4. Calculate the ratio of their volumes.जी रिजल्ट ऑफ टू राइट सर्कुलर सिलेंडर आर इन द रेश्यो ऑफ 2.2 स्टेट्स एंड द राइट आर इन द रेश्यो ऑफ फर्स्ट फॉर द रेश्यो ऑफ द वॉल्यूम ​

Answer 1

${\huge{\underline{\purple{\bf\tt{Question:} } }}}$

The radii of two right circular cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 4. Calculate the ratio of their volumes.

${\boxed{\underline{\green{\bf\tt{Given:} } }}}$

Let the radii be R and r and heights be H and h

The ratio is

R:r=2:3

H:h=5:4

${\boxed{\underline{\orange{\bf\tt{Solution:} } }}}$

Formulae for volume of cylinder $\boxed{\pi r^2h}$

Volume of the cylinder having radius R and height H = $\pi R^2H \: \: \: = \pi 2^25=20 \pi$

Volume of the cylinder having radius r and height h = $\pi r^2h = \pi 3^24=36 \pi$

Now, the ratio of the volumes:

$\sf \mapsto\frac{20 \pi} {36 \pi} \mapsto \frac{20 \cancel{\pi}} {36 \cancel{ \pi}} \\\\\sf \mapsto \frac{20}{36} \implies \frac{5}{9}$

Hence, the ratio of their volumes is 5:9