Assam Board Solutions for Chapter: Surface Areas and Volumes, Exercise 5: Exercise 13.5

A copper wire$,3 \mathrm{m}\mathrm{m}$ in diameter, is wound about a cylinder whose length is $12 \mathrm{c}\mathrm{m}$, and diameter $10 \mathrm{c}\mathrm{m}$, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of copper to be $8.88 \mathrm{g} \mathrm{p}\mathrm{e}\mathrm{r} \mathrm{c}{\mathrm{m}}^3$.

A right triangle, whose sides are $3 \mathrm{c}\mathrm{m}$ and $4 \mathrm{c}\mathrm{m}$ ( other than hypotenuse ) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. ( Choose value of $\mathrm{}\mathrm{\pi }$ as found appropriate )

A cistern, internally measuring $150 \mathrm{c}\mathrm{m}\times 120 \mathrm{c}\mathrm{m}\times 110 \mathrm{c}\mathrm{m}$, has $129600 \mathrm{c}{\mathrm{m}}^3$ of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each brick being $22.5 \mathrm{c}\mathrm{m}\times 7.5 \mathrm{c}\mathrm{m}\times 6.5 \mathrm{c}\mathrm{m}$?

In one fortnight of a given month, there was a rainfall of $10 \mathrm{c}\mathrm{m}$ in a river valley. If the area of the valley is $97280 \mathrm{k}{\mathrm{m}}^2$, show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each $1072 \mathrm{k}\mathrm{m}$ long, $75 \mathrm{m}$ wide and $3 \mathrm{m}$ deep.

An oil funnel made of tin sheet consists of a $10 \mathrm{c}\mathrm{m}$ long cylindrical portion attached to a frustum of a cone. If the total height is $22 \mathrm{c}\mathrm{m}$, diameter of the cylindrical portion is $8 \mathrm{c}\mathrm{m}$ and the diameter of the top of the funnel is $18 \mathrm{c}\mathrm{m}$, find the area of the tin sheet required to make the funnel (see Fig.).

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Derive the formula for the curved surface area and total surface area of the frustum of a cone, using the symbols as explained.

Derive the formula for the volume of the frustum of a cone, using the symbols as explained.