EXERCISE

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. $(\mathrm{\pi }=3.14)$ 

A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is $6 \mathrm{cm}$ and its height is $4 \mathrm{cm}$. Determine the volume of the toy. Also, find the mass if the mass of $1 {\mathrm{cm}}^3$ of wood is $3.5 \mathrm{g}$.

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.

A toy is in the form of right circular cylinder with a hemisphere on one end and cone on the other end. The height and radius of base of cylindrical part are $15 \mathrm{cm}$ and $7 \mathrm{cm}$ respectively. The radius of hemisphere and base of the conical part are same as that of the cylindrical. Calculate the volume of the toy, if the height of the cone is $14 \mathrm{cm}$. Write the answer upto two decimal places.

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.

A wooden article was made by scooping out a hemisphere from each end of a cylinder. If the height of the cylinder is $20 \mathrm{cm}$, and its base is of diameter $14 \mathrm{cm}$, find the volume of the article when it is ready. Write the answer upto two decimal places.

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

A steel pulley was made from two big equal cylinders stuck at the ends of a small cylinder as shown in the Fig. If the weight of the pulley is $W\hspace{0.17em}\mathrm{kg}$, where $1 {\mathrm{cm}}^3$ of steel weighs $7.6 \mathrm{grams}$, then find the value of $W$ (Write the answer up to three decimal places).