Question

A cylinder of volume 150 cu. cm is placed with a cone, whose height is 4 cm. If the height of cone and cylinder is equal, then find the total volume of shape formed by the combination of cylinder and cone.

Answer 1

Given, Volume of cylinder $=150$ cu.cm
Height of cylinder $=$ Height of cone $=4cm$
By the formula of volume of cylinder we know,
$$\begin{array}{cc}& V_1=\pi r^{2}h\\ & 150=\pi r^2\left(4\right)\\ & r^2=150/4\pi \dots \dots \left(1\right)\end{array}$$
Now, volume of cone is given by:
$$V_2=1/3\pi r^{2}h$$
By putting the value of $r^2$ from eq. 1 we get;
Therefore, $V_2=1/3\pi \left(150/4\pi \right)$ (4)
On solving the above, we get;
$$V_2=50\text{cu.cm.}$$
Therefore, the total volume of the combined solids, $V=V_1+$ $V_2=150+50=200$ cu.cm.