Name: Conversion of Solids
Uploaded: 2019-07-19
Duration: 5 min 33 s
Description: What happens when a goldsmith heats a gold bar to create something? The gold bar's shape gets changed. But what about its volume? Does it change too? Find ou...

Question

A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are $2.1 m$ and $4 m$ respectively, and the slant height of the top is $2.8 m$ , 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 $₹ 350 p e r m^{2}$ . (Note that the base of the tent will not be covered with canvas.)

Accepted Answer

It is given that,

The height $(h)$ of the cylindrical part $= 2 .1 m$

The diameter of the cylindrical part $= 4 m$

Therefore, the radius of the cylindrical part $= 2 m$

The slant height $(l)$ of conical part $= 2 .8 m$

The area of canvas used for making the tent $= C S A$ of conical part $+ C S A$ of cylindrical part

$= π rl + 2 πrh$

$= π \times 2 \times 2 .8 + 2 π \times 2 \times 2 .1$

$= 2 π [2.8 + 2 \times 2.1] = 2 π [2.8 + 4.2] = 2 \times \frac{22}{7} \times 7$

$= 44 m^{2}$

Cost of $1 m^{2}$ canvas $= ₹ 350$

Cost of $44 m^{2}$ canvas $= 44 \times 350 = ₹ 15400$

Hence, it will cost $₹ 15400$ for making the tent.

Important Questions on Surface Areas and Volumes

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