A wooden article was made by scooping out a hemisphere from each end of a cylinder, as shown in the figure. The height of the cylinder is $20 \mathrm{cm}$ and its base is of diameter $7 \mathrm{cm}$ If the total surface area of the article when it is ready is $k {\mathrm{cm}}^2$, then find the value of $k$. ( Take $\pi =\frac{22}{7}$)

 

A cylindrical vessel with internal diameter $10 \mathrm{cm}$ and height $10.5 \mathrm{cm}$is full of water. A solid cone of base diameter $7 \mathrm{cm}$ and height $6 \mathrm{cm}$ is completely immersed in water. Find the volume of water (i) displaced out of the cylinder (ii) left in the cylinder. (Take $\mathrm{\pi }=\frac{22}{7}$)

A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is $21 \mathrm{cm}$ and its volume is $\frac{2}{3}$ of the volume of the hemisphere, calculate the height of the cone and surface area of the toy. (Use $\mathrm{\pi }=\frac{22}{7}$ )