A carpenter, Abdullah prepared a model which is in the form of a cylinder with hemispherical ends. The total height of the solid is $19 \mathrm{cm}$ and the diameter of the cylinder is $7 \mathrm{cm}$. Find the volume and surface area of the solid.​

A vessel is in the form of an inverted cone. Its height is $8 \mathrm{cm}$ and radius of its top, which is open, is $5 \mathrm{cm}$. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius$0.5 \mathrm{cm}$ are dropped into the vessel, one fourth of the water flows out. Find the number of lead shots dropped in the vessel.

The difference between the outside and inside surfaces of a cylindrical metal pipe which is $14 \mathrm{cm}$ long is $44 {\mathrm{cm}}^2$. If the pipe is made of $99 {\mathrm{cm}}^3$ of metal, find the outer and inner radii of the pipe. [Take $\mathrm{\pi }=\frac{22}{7}$]

A solid iron pole having cylindrical portion $110 \mathrm{cm}$ high and of base diameter $12 \mathrm{cm}$ is surmounted by a cone $9 \mathrm{cm}$ high. Find the mass of the pole, given that the mass of $1 {\mathrm{cm}}^3$ of iron is $8 \mathrm{gm}$. [Take $\mathrm{\pi }=\frac{22}{7}$]

A right triangle, whose sides are $15 \mathrm{cm}$ and $20 \mathrm{cm}$ is made to revolve about its hypotenuse. Find the volume and the surface area of the double cones so formed. $(\mathrm{\pi }=3.14)$ 

From a solid cylinder whose height is $8.2 \mathrm{cm}$ and the diameter $3.5 \mathrm{cm}$ a conical cavity of the same height and the same diameter is hollowed out. Find the volume of the remaining solid to the nearest ${\mathrm{cm}}^3$ .

If the answer is k ${\text{cm}}^3$ , then write the value of k.

If the answer is k ${\text{cm}}^3$ , then write the value of k.

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is $15 \mathrm{mm}$ and the diameter of the capsule is $7 \mathrm{mm}$. Find the volume of medicine contained in it. Write the answer upto two decimal places.

If the answer is k ${\text{mm}}^3$ , then write the value of k.