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​



Plz Don't spam

Answer 1

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

Answer 2

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

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

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$\sf\star{As \: we \: know \: that,}$

• Volume of Cylinder =

$\frak{\pi r^2 h}$

• Volume of Sphere =

$\frak{\dfrac{4}{3} \pi r^3}$

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

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

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

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