Question

The base radii of two cylinders are in the ratio 3:4 and their heights in the ratio 5:2. The volume of the first cylinder is 300 $c{m}^3$. What is the volume of the second?

• A. $220.55c{m}^3$
• B. $213.33c{m}^3$
• C. $219.16c{m}^3$
• D. $217c{m}^3$

Answer 1

The correct option is B

$213.33c{m}^3$

Let the radius of cylinder 1 = $r_1$ and height = $h_1$

Let the radius of cylinder 2 = $r_2$ and height = $h_2$

$\frac{Volumeofcylinder1}{Volumeofcylinder2}=\frac{\pi r_1^2{h}_1}{\pi r_2^2{h}_2}$
Given: $\frac{r_1}{r_2}=\frac{3}{4},\frac{h_1}{h_2}=\frac{5}{2}$

$\frac{v_1}{v_2}=\frac{\pi r_1^2{h}_1}{\pi r_2^2{h}_2}={\left(\frac{r_1}{r_2}\right)}^2\left(\frac{h_1}{h_2}\right)$
$\frac{v_1}{v_2}={\left(\frac{3}{4}\right)}^2\left(\frac{5}{2}\right)=\frac{45}{32}$

Now, $v_1=300c{m}^3$

Hence $\frac{300}{v_2}=\frac{45}{32}$

$v_2=\frac{300\times 32}{45}=\frac{3\times 100\times 8\times 4}{9\times 5}=213.33c{m}^3$