Question

Once four friends Rahul, Arun, Ajay and Vijay went for a picnic at a hill station. Due to
peak season, they did not get a proper hotel in the city. The weather was fine so they
decided to make a conical tent at a park. They were carrying 300 m2 cloth with them. As
shown in the figure they made the tent with height 10 m and diameter 14 m. The
remaining cloth was used for the floor.
guide.con
or CBSE students
How much
cloth was used to the floor?​

Answer 1

Given:

Once four friends Rahul, Arun, Ajay and Vijay went for a picnic at a hill station. Due to peak season, they did not get a proper hotel in the city. The weather was fine so they decided to make a conical tent at a park.

They were carrying 300 m² cloth with them.

They made the tent with height 10 m and diameter 14 m

The  remaining cloth was used for the floor.

To find:

How much cloth was used to the floor?​

Solution:

We know,

$\bigstar \boxed{\bold{Curved\:surface \:area \:of\: a\:cone = \pi r l }}\bigstar$

The area of cloth the 4 friends were carrying with them was = 300 m²

The height of the conical tent = 10 m

The diameter of the conical tent = 14 m

So, the radius of the tent, r = $\frac{14}{2}$ = 7 m

The slant height "l" of the conical tent is,

= $\sqrt{ h^2 + r^2} = \sqrt{10^2 + 7^2} = \sqrt{149} = 12.2 \:m$

∴ The required area of the cloth for making the tent is,

= Curved Surface area of the conical tent

= $\pi r l$

= $\frac{22}{7} \times 7 \times 12.2$

= $268.4\:m^2$

Now,

The remaining area of cloth used to the floor was,

= 300 m² - 268.4 m²

= 31.6 m²

Thus, 31.6 m² of cloth was used to the floor.

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Answer 2

Given : 300 sq.m cloth used to make tent ,.

conical tent with height 10m and diameter 14m.

The remaining cloth was used for the floor​

To find :

 What is the slant height of the tent?

   What was the volume of the tent?

 What was the area of the floor?

Solution:

area of the floor = π7²

= (22/7) (7)²

= 154   m²

conical tent with height 10m and diameter 14m.

=> radius = 14/2 = 7 m

h = 10 m

Formula for slant Height = √r² + h²

slant height L = √7² +10² = √149 m

= 12.2 m

 

Curved surface Area = πRL

=(22/7) ( 7)12.2

= 268.4  m²

Cloth used for floor = 300 -  268.4 = 31.6 m²

Total Surface area =  300 Sq m as that much cloth was available

 

volume of the tent = (1/3)πR²h

= (1/3)(22/7)*7²*10

=  513.3 m³

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