Two cylindrical vessels are filled with oil. Their radii are $15 c m, 12 c m$ and heights $20 c m, 16 c m$ respectively. Find the radius of a cylindrical vessel $21 c m$ in height, which will just contain the oil of the two given vessels.

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Solution

Volume of new cylindrical vessel $=$ Sum of volumes of two cylindrical vessels
$\Rightarrow π r^{2} H = π [R_{1}^{2} H_{1} + R_{2}^{2} H_{2}] \Rightarrow R^{2} \times 21 = {(15)}^{2} \times 20 + {(12)}^{2} \times 16$
$\Rightarrow R^{2} = 324 \Rightarrow R = \sqrt{324} = 18 c m$

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Two cylindrical vessels are filled with oil. Their radii are 15cm,12cm and heights 20cm,16cm respectively. Find the radius of a cylindrical vessel 21cm in height, which will just contain the oil of the two given vessels.

Volume of new cylindrical vessel = Sum of volumes of two cylindrical vessels⇒πr2H=π[R21H1+R22H2]⇒R2×21=(15)2×20+(12)2×16⇒R2=324⇒R=√324=18cm

Two cylindrical vessels are filled with oil. Their radii are $15 c m, 12 c m$ and heights $20 c m, 16 c m$ respectively. Find the radius of a cylindrical vessel $21 c m$ in height, which will just contain the oil of the two given vessels.

Volume of new cylindrical vessel $=$ Sum of volumes of two cylindrical vessels
$\Rightarrow π r^{2} H = π [R_{1}^{2} H_{1} + R_{2}^{2} H_{2}] \Rightarrow R^{2} \times 21 = {(15)}^{2} \times 20 + {(12)}^{2} \times 16$
$\Rightarrow R^{2} = 324 \Rightarrow R = \sqrt{324} = 18 c m$