Question

a conical tent is 12 m high and base radius is 16 find the cost of canvas required to make the tent if cost if 1m² is 70 rupees​

Answer 1

Answer:

Rs.70336

Explanation:

A conical tent of,

• height (h) = 12m
• radius of the base (r) = 16m

Find the cost of canvas required to make the tent is the rate is Rs.70/m²

Here,

We need to find the curved surface area of the tent to find out the total cost.

∴ Curved surface area of the tent is given by,

$\boldsymbol{ = \pi rl}$

Finding $\boldsymbol l$ (slant height) :-

$= \sqrt{ {r}^{2} + {h}^{2} }$

$= \sqrt{ {(16)}^{2} + {(12)}^{2} }$

$= \sqrt{256 + 144}$

$= \sqrt{400}$

$\rm = 20 m$

Calculating the curved surface area,

$= \pi rl$

$= 3.14 \times 16 \times 20$ [taking π as 3.14]

$\rm = 1004.8 {m}^{2}$

∴ Curved surface area is 1004.8m²

Now then,

Total cost for construction :-

= rate × area

= 70 × 1004.8

= Rs.70336

∴ Required answer: Rs.70,336

___________________________

Formulae:

• Slant height = $= \sqrt{ {r}^{2} + {h}^{2} }$
• Curved surface area = $\boldsymbol{ = \pi rl}$

Where,

• r denotes the base radius.
• h is the height.

Answer 2

Given :

Height of the tent (h) = 12 m

Radius of the base (r) = 16 m

The cost of 1 m² canvas

• = 70 Rs

To Find :

• The Slant height

• Cost of canvas required to make the tent

Formula used :

$\rm \: l = \sqrt{ {h}^{2} + {r}^{2} }$

$\rm \: Curved \: surface \: area \: of \: cone = \pi \: r \: l \:$

Solution :

$\rm \: \because \: The \: Slant \: height ,l = \sqrt{ {h}^{2} + {r}^{2} }$

$\rm \implies \: \sqrt{ {12}^{2} + {16}^{2} \: m }$

$\rm \implies \: \sqrt{144 + 256 \: m}$

$\rm \implies \: \sqrt{400}$

$\rm \implies \: 20 \: m$

Thus,

• Required slant height of the tent is 20 m

$\rm \: \because \: The \: Curved \:Surface \: area \: of \: cone ,l = \pi \: r \: l$

$\rm \: \therefore\: The \: Area \: of \: canvas \: required ,$

$\rm \implies \: \dfrac{22}{7} \times 16 \times 20 \: {m}^{2}$

$\implies \: \dfrac{7040}{7}$

$\rm \: \therefore \: The \: cost \: of \: canvas$

$\implies \rm \: \: 70 \: Rs \times \dfrac{7040}{7}$

$\implies \rm\: 10 \: Rs \: \times 7040$

$\rm \implies \boxed{70,400 \: Rs}$