Question

Find the length of canvas 1.1 m wide required to build a conical tent of height 14m and the floor
area 346.5 sq m.​

Answer 1

Answer:

Given, h=14 m and floor area =346.5 m

2

.

We know, the base of a cone is a circle.

Then, ⇒πr

2

=346.5

⇒r

2

=346.5×

22

7

=110.25

⇒r=10.5.

∴ Slant height, l=

r

2

+h

2

=

(10.5)

2

+(14)

2

=

110.25+196

=

306.25

=17.5 m.

∴ Curved surface area =πrl

=

7

22

×10.5×17.5=

7

4042.5

m

2

.

Width of cloth =1.1 m.

∴ Length of cloth required =

1.1

(

7

4042.5

)

=

7.7

4042.5

=525m.

Hence, 525 m length of canvas is required to build the conical tent.

Step-by-step explanation:

Given, h=14 m and floor area =346.5 m

2

.

We know, the base of a cone is a circle.

Then, ⇒πr

2

=346.5

⇒r

2

=346.5×

22

7

=110.25

⇒r=10.5.

∴ Slant height, l=

r

2

+h

2

=

(10.5)

2

+(14)

2

=

110.25+196

=

306.25

=17.5 m.

∴ Curved surface area =πrl

=

7

22

×10.5×17.5=

7

4042.5

m

2

.

Width of cloth =1.1 m.

∴ Length of cloth required =

1.1

(

7

4042.5

)

=

7.7

4042.5

=525m.

Hence, 525 m length of canvas is required to build the conical tent.

Answer 2

=

$\pi \: {r}^{2} = 346.5$

${r}^{2} = (346.5 \times \frac{22}{7} ) \\ {r}^{2} = \frac{441}{4}$

${r}^{2} = \frac{21}{2}$

$l \: = \sqrt{ {r}^{2} + {h}^{2} } \\ = \sqrt{ \frac{441}{4} + {(14)}^{2} } \\ = \sqrt{ \frac{1225}{4} } \\ = \frac{35}{2}$

So , area of canvas needed :

$\pi \: rl \: = ( \frac{22}{7} \times \frac{21}{2} \times \frac{35}{2} ) {m }^{2} \\ = ( \frac{33 \times 35}{2} ) {m}^{2}$

Length of canvas :

$= ( \frac{33 \times 35}{2 \times 1.1} m$

$= 525 {m}^{2}$