A conical tent is $ 10 \mathrm{~m} $ high and the radius of its base is $ 24 \mathrm{~m} $. Find
(i) slant height of the tent.
(ii) cost of the canvas required to make the tent, if the cost of $ 1 \mathrm{~m}^{2} $ canvas is $ Rs.\ 70 $.

AcademicMathematicsNCERTClass 9

Given:

A conical tent is $10\ m$ high and the radius of its base is $24\ m$. 

The cost of $1\ m^2$ canvas is $Rs.\ 70$.

To do:

We have to find the slant height of the tent and the cost of the canvas required to make the tent.

Solution:

Height of the conical tent $h= 10\ m$

Radius of the base $(r) = 24\ m$

Therefore,

Slant height of the tent $(l)=\sqrt{r^{2}+h^{2}}$

$=\sqrt{(24)^{2}+(10)^{2}}$

$=\sqrt{576+100}$

$=\sqrt{676}$

$=26 \mathrm{~m}$

The curved surface area of the conical tent $=\pi r l$

$=\frac{22}{7} \times 24 \times 26$

Rate of $1 \mathrm{~m}^{2}$ canvas used $=Rs.\ 70$

This implies,

The total cost of the tent$=Rs.\ \frac{22}{7} \times 24 \times 26 \times 70$

$= Rs.\ 137280$

Therefore,

The slant height of the tent and the total cost of the tent used are $26 \mathrm{~m}$ and $Rs.\ 137280$ respectively.

raja
Updated on 10-Oct-2022 13:46:36

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