Question

The circumference of the base of a 8m high conical tent is 264/7m^2 . The area of canvas required to make the tent is

Answer 1

Answer :

$\large \sf \implies 188.5 m^2$

Solution :

Given :

• circumference of Base = 8m
• Height = 264/7m

To Find :

Area of Canvas required to make tent.

$\large \red \bigstar \boxed{\sf Circumference \: of \: circle = \: 2 \pi r }$

so,

$\implies 2 \pi r = \frac{264}{7} \\ \implies 2 \times \frac{22}{\cancel{7}} \times r = \frac{264}{\cancel{7}} \\ \implies \boxed{\mathfrak{r= 6m}}$

$\large \red \bigstar \boxed{\sf Surface \: area = \: \pi r l}$

Where,

• l = slant height
• r = radius

$\large \red \bigstar \boxed{\sf slant \: height ,l = \: \sqrt{r^2 + h^2}}$

$\sf l = \: \sqrt{r^2 + h^2} \\ \implies \sqrt{6^2 + 8^2} \\ \implies \sqrt{36 + 64} \\ \implies \boxed{\mathfrak{l = 10m}}$

so,

Area of Canvas required =

$\: \: \: \: \: \: \: \: \: \implies \pi \times r \times l$

$\: \: \: \: \: \: \: \: \: \implies \pi \times 6 \times 10 \\ \implies \frac{22}{7} \times 6 \times 10 \\ \\ \implies \frac{1320}{7} \\ \implies 188.5 m^2$

Therefore,

Area of canvas required to make the tent is 188.5m².

Answer 2

Answer:

Step-by-step explanation:

Let r m be the radius of the base h m be the height and l m be the slant height of the cone Then

Circumference=44 metres

⇒2πr=44⇒2×

7

22

​

×r=44⇒r=7

metres It is given that h=10 metres

∴l

2

=r

2

+h

2

⇒l=

r

2

+h

2

​

=

49+100

​

=

149

​

=12.2m

Now surface area of the tent =πrl

7

22

​

×7×12.2m

2

=268.4m

2

∴ Area of the canvas used =268.4m

2

It is given that the width of the canvas is 2 m

∴ Length of the canvas used==

width

area

​

=

2

268.4

​

=134.2m