Question

If a solid cylindrical vessel of base radius 5 cm and height 10 cm be melted into a solid conical vessel of the same base and height, then the number of such cones is

• A. 2
• B. 3
• C. 4
• D. 6

Answer 1

The correct option is B 3

Given that,base$\left(5cm\right)$ and height $(H=10m)$ of solid cylindrical vessel

Now, radius of cylindrical vessel =half of diameter $\left(R\right)=2.5m$

Let, the radius od conical vessel =r and height $=h$

Now, required number of cones =volume of cylindrical vessel/volume of conical vessel

$=\frac{\pi .R^2.H}{\frac{1}{3}\pi .r^2.h}=\frac{R^2.H}{\frac{1}{3}{r}^2.h}$

$=\frac{{\left(2.5\right)}^2\times 10}{\frac{1}{3}\times {\left(2.5\right)}^2\times 10}$ (given that same base and height of cylindrical vessel an conical vessel)

$=3$

Hence, this is the answer.

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