A hollow sphere of internal and external radii $6\mathrm{cm}$ and $8\mathrm{cm}$ respectively, is melted and recast into small cones of base radius $2\mathrm{cm}$ and height $8\mathrm{cm}$. Find the number of cones.

A corn cob (see figure), shaped somewhat·like a cone, has the radius of its broadest end as $2.1 \mathrm{cm}$ and length as $20 \mathrm{cm}$. If each $1 {\mathrm{cm}}^2$ of the surface of the cob carries an average of four grains, then how many grains you would find on the entire cob? [Take$\mathrm{\pi }=\frac{22}{7}$ ]

A semi-circle is drawn, which is passing through the points $\mathrm{A}(3,0)$, $\mathrm{B}(0,3)$ and $\mathrm{C}(-3,0)$. [Take$\mathrm{\pi }=3.14$)

When we rotate this figure along the side $\mathrm{AC}$, then write the name of the figure formed and then the space occupied by this will be

A semi-circle is drawn, which is passing through the points $\mathrm{A}(3,0)$, $\mathrm{B}(0,3)$ and $C(-3,0)$. [Take$\mathrm{\pi }=3.14$)

When we rotate this figure along the side $\mathrm{BO}$, then write the name of the figure formed and then the space occupied by this will be $k {\mathrm{cm}}^3$. Find $k$.

A pen-stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are $15 \mathrm{cm}\times 10 \mathrm{cm}\times 3.5 \mathrm{cm}$. The radius of each of the depressions is $0.5 \mathrm{cm}$ and the depth is $1.4 \mathrm{cm}$. Then, the volume of wood in the entire stand is $k {\mathrm{cm}}^3$. Find $k$. [Take$\mathrm{\pi }=\frac{22}{7 }$]