Exercise 12.1

Two cubes each of volume $64 \text{ cm}^3$ are joined end to end. Find the surface area of the resulting cuboid.

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is $14$ cm and the total height of the vessel is $13$ cm. Find the inner surface area of the vessel.

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

A cubical block of side $7$ cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

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. 12.10). The length of the entire capsule is $14$ mm and the diameter of the capsule is $5$ mm. 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 $2.1 \text{ m}$ and $4 \text{ m}$ respectively, and the slant height of the top is $2.8 \text{ m}$, 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 $\text{₹ } 500$ per $\text{m}^2$. (Note that the base of the tent will not be covered with canvas.)

From a solid cylinder whose height is $2.4$ cm and diameter $1.4$ cm, 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 $\text{cm}^2$.

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. 12.11. If the height of the cylinder is $10$ cm, and its base is of radius $3.5$ cm, find the total surface area of the article.