Question

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Find the Volume of Firgure A.

Answer 1

Answer:

1375 cubic units.          

Step-by-step explanation:

Let $r_1$, $h_1$ and $V_1$ be radius, height and volume of our large cylinder respectively. Let $r_2$, $h_2$ and $V_2$ be radius, height and volume of our small cylinder respectively.

We have been given that both our given cylinders in graph are similar, therefore, the ratios between their radius, height and volume will be same.

$\frac{r_1}{h_1} =\frac{r_2}{h_2}$

We can also represent this relation as:

$\frac{h_1}{h_2} =\frac{r_1}{r_2}$  

Since corresponding sides of similar figures are always in the same proportion, so the proportion between volume of our cylinders also will be same.    

$\frac{V_1}{V_2} =\frac{\pi (r_1)^{2} h_1}{\pi(r_2)^{2}h_2}$

Upon cancelling out pi from numerator and denominator we will get,     

$\frac{V_1}{V_2} =\frac{(r_1)^{2} h_1}{(r_2)^{2}h_2}$

Upon using the relation $\frac{h_1}{h_2} =\frac{r_1}{r_2}$   in volume proportion we will get,  

$\frac{V_1}{V_2} =\frac{(r_1)^{2}\times r_1}{(r_2)^{2}\times r_2}$  

$\frac{V_1}{V_2} =\frac{(r_1)^{3} }{(r_2)^{3}}$  

Upon substituting our given values in this proportion we will get,      

$\frac{V_1}{88} =\frac{(5)^{3} }{(2)^{3}}$

$\frac{V_1}{88} =\frac{125}{8}$  

$V_1 =\frac{125}{8}\times 88$

$V_1 =125\times 11$              

$V_1=1375$

Therefore, the volume of large cylinder will be 1375 cubic units.