Exercise 13.1

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is $14 \mathrm{c}\mathrm{m}$ and the total height of the vessel is $13 \mathrm{c}\mathrm{m}$. Find the inner surface area of the vessel.

A toy is in the form of a cone of radius $3.5 \mathrm{c}\mathrm{m}$ mounted on a hemisphere of same radius. The total height of the toy is $15.5 \mathrm{c}\mathrm{m}$. Find the total surface area of the toy.

A cubical block of side $7 \mathrm{c}\mathrm{m}$ is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.$\left(\mathrm{use}\pi =\frac{22}{7}\right)$

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter $l$ of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig.). The length of the entire capsule is $14 \mathrm{m}\mathrm{m}$ and the diameter of the capsule is $5 \mathrm{m}\mathrm{m}$. Find its surface area.

A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are $2.1 \mathrm{m}$ and $4 \mathrm{m}$ respectively, and the slant height of the top is $2.8 \mathrm{m}$, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of $\mathrm{₹}500 \mathrm{p}\mathrm{e}\mathrm{r} {\mathrm{m}}^2$. (Note that the base of the tent will not be covered with canvas.) 

From a solid cylinder whose height is $2.4 \mathrm{c}\mathrm{m}$ and diameter $1.4 \mathrm{c}\mathrm{m}$, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest ${\mathrm{c}\mathrm{m}}^2$.

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in figure. If the height of the cylinder is $10 \mathrm{c}\mathrm{m}$, and its base is of radius $3.5 \mathrm{c}\mathrm{m}$, find the total surface area of the article.