Question

What is the ratio of the sum of volumes of two-cylinder of radius 1 cm and height 2 cm each

to the volume of a sphere of radius 3 cm?


Need help with this question, the answer I keep getting is 1:9​

Answer 1

$\frak{Given} \begin{cases} \sf Radius\:of\:two\:cylinders\: = \frak{1\:cm} & \\ \\\sf Height\:of\:two\:cylinders\: = \frak{2\:cm}& \\ \\ \sf Radius\:of\:sphere\: = \frak{31\:cm}&\end{cases}$

Need to find: The ratio of the sum of volumes of two cylinder to the volume of a sphere.

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$\star$ As we know that,

• Volume of Cylinder = $\frak{\pi r^2 h}$

• Volume of Sphere = $\frak{\dfrac{4}{3} \pi r^3}$

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$\bigstar\:{\underline{\sf{\pmb{According\:to\:the\:Question\::}}}}$

• There are two cylinder of equal radius and equal Height. So, We can say that there volume is also equal.

Now, We can calculate the ratio of volume of those two cylinders to the volume of sphere as,

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$:\implies \frak{\dfrac{2 \times (Volume\:of\:cylinder)}{ (Volume\:of\:sphere)}}\\\\\\ :\implies\sf \dfrac{2 \times \bigg( \dfrac{22}{7} \times (1)^2 \times 2 \bigg)}{ \dfrac{4}{3} \times \dfrac{22}{7} \times (3)^3}\\\\\\ :\implies\sf \dfrac{2 \times \bigg( \dfrac{22}{7} \times 1 \times 2 \bigg)}{ \dfrac{4}{\cancel{3}} \times \dfrac{22}{7} \times \cancel{27}}\\\\\\ :\implies\sf \dfrac{2 \times \dfrac{22}{7} \times 2}{4 \times \dfrac{22}{7} \times 9}\\\\\\:\implies\sf \dfrac{4 \times \cancel{\dfrac{22}{7}}}{4 \times \cancel{\dfrac{22}{7}} \times 9}\\\\\\ :\implies\sf \dfrac{\cancel{4}}{\cancel{4} \times 9}\\ \\\\ :\implies{\boxed{\underline{ \frak{ \purple{ \dfrac{1}{9}}}}}}\:\bigstar$

$\therefore\:{\underline{\sf{Hence\:the\:required\:ratio\:is\: {\textsf{\textbf{1:9}}}.}}}$

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The answer you're getting is correct mate! :)

Answer 2

Given :-

• Radius = 1 cm
• Height = 2 cm
• Radius = 3 cm

To Find :-

Ratio of Cylinder to Sphere

Now

We know that

$\large \sf Volume = \pi r^{2} h$

Now

Volume of two cylinder = 2(22/7 × 1 × 1 × 2)

=> V = 2(22/7 × 2)

=> V = 2(44/7)

=> V = 88/14

Now

Volume of sphere = 4/3 × 22/7 × 3 × 3 × 3

=> Volume = 4 × 22/7 × 9

=> Volume = 88/7 × 9

=> Volume = 792/7

Now

Ratio = (88/14)/(792/17)

Ratio = 88 × 17/14 × 792

Ratio = 1496/11088

Ratio = 1:9