​Karthik an engineering student is designing a model which is shaped  like a cylinder with two equal cones attached at it's two ends. The diameter of the model is 3.5cm and it's length is 18cm. If each cone has a height of 4cm, find the volume of the model that Karthik made.
Please don't provide a link to a similar question, as I know the method, and I just wanted to check my answer.
Thank You.

Dear Student,

Please find below the solution to the asked query:

We have our diagram as :


Given  : Height of cylindrical part  =  10 cm And Height of conical part  =  4 cm 
And 
Radius of base  =  3.5 cm 

So, 
Volume of model   =  Volume of cylindrical part + 2 ( Volume of Conical part )

We know :
Volume of Cylinder  = $\mathrm{\pi } {\mathrm{r}}^2\mathrm{h}$ and Volume of Cone  = $\frac{\mathrm{\pi } {\mathrm{r}}^2 \mathrm{h}}{3}$
So, 
$$\begin{gathered} \mathrm{Volume} \mathrm{of} \mathrm{model} = \frac{22}{7} \times 3.5 \times 3.5 \times 10 + 2 \left(\frac{{\displaystyle \frac{22}{7} \times 3.5 \times 3.5 \times 4}}{3}\right) \\ \Rightarrow \mathrm{Volume} \mathrm{of} \mathrm{model} = \frac{22}{2} \times 3.5 \times 10 + 2 \left(\frac{{\displaystyle 11 \times 3.5 \times 4}}{3}\right) \\ \Rightarrow \mathrm{Volume} \mathrm{of} \mathrm{model} =11 \times 3.5 \times 10 + 2 \left(\frac{{\displaystyle 154}}{3}\right) \\ \Rightarrow \mathrm{Volume} \mathrm{of} \mathrm{model} =385 + \frac{{\displaystyle 308}}{3} \\ \Rightarrow \mathrm{Volume} \mathrm{of} \mathrm{model} =385 + 102.666 \\ \mathbf{\Rightarrow }\mathbf{Volume}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{model}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{487}\mathbf{.}\mathbf{666}\mathbf{ }\mathbf{\approx }\mathbf{ }\mathbf{487}\mathbf{.}\mathbf{67}\mathbf{ }\mathbf{ }{\mathbf{cm}}^{\mathbf{3}}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)} \end{gathered}$$

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