Question

Plz solve all champions!!!

Answer 1

In order to find the Area of the Canvas required to make the Tent :

1. We need to find the Curved Surface Area of the Cylindrical Part

2. We need to find the Curved Surface Area of the Conical Part

3. Add Both the Parts (i.e.) Adding both Curved Surface Area of the Cylindrical Part and Curved Surface Area of the Conical Part

As the Cylindrical Part of the Tent does not include the Area's of Circles which are at the Top and the Bottom of the Tent.

Curved Surface Area of the Cylindrical Part will be : 2πr × Height

Given : The Diameter of the Base of the Tent : 48 m

It means the Radius of the Cylindrical Part will be $\bf{: (\frac{48}{2}) = 24\;m}$

Given : The Height of the Cylindrical Part = 15 m

⇒ Curved Surface Area of the Cylindrical Part : 2π(24)(15) = 720π

As the Conical part of the Tent does not include the Area of Circle which is at the Bottom.

Curved Surface Area of Conical Part will be : πr × Slant Height

But, The Slant Height of the Conical Part is not given to us. How can we find out the Curved Surface Area of the Conical Part then?

Let us look into the Question Once More and Find out something which can help us in calculating Slant Height.

Given : The Total Height of the Tent is 33 m

It means the Height of the Conical Part will be the Difference between Total Height of the Tent and Height of the Cylindrical Part of the Tent.

⇒ Height of the Conical Part : (33 - 15) = 18 m

Now, If we Imagine the Conical Part of the Tent : We can Notice that the Slant Height of the Conical Part is the Hypotenuse of the Right Angled Triangle formed by the Height of the Conical Part and The Radius of the Base of the Tent.

Now, According to Pythagorean Theorem :

(Slant Height of the Conical Part)² = (Height of the Conical Part)² + (Radius of the Base of the Tent)²

⇒ (Slant Height of the Conical Part)² = 18² + 24²

⇒ (Slant Height of the Conical Part)² = (324 + 576) = 900

⇒ Slant Height of the Conical Part = 30 m

⇒ Curved Surface Area of Conical Part = π(24)(30) = 720π

Total Curved Surface Area of both Cylindrical Part and Conical Part of the Tent = (720π + 720π) = 1440π = 4523.89 m²

⇒ Area of the Canvas required to make the Tent = 4523.89 m²

In order to find the Volume of the Air in the Tent :

1. We need to Find the Volume of the Cylindrical Part

2. We need to Find the Volume of the Conical Part

3. Add both the Parts (i.e.) Adding Both, The Volume of the Cylindrical Part and the Volume of Conical Part

We know that, Volume of Cylinder is given by : πr² × Height

⇒ Volume of the Cylindrical Part of the Tent : π(24)²(15) = 8640π

⇒ We know that, Volume of Cone is given by $\bf{: \frac{\pi r^2h}{3}}$

⇒ Volume of the Conical Part of the Tent $\bf{: [\frac{\pi(24)^2(18)}{3}] = 3456\pi}$

Total Volume of both Cylindrical Part and Conical Part of the Tent is : (8640π + 3456π) = 12096π = 38000.7 m³

⇒ The Volume of Air in the Tent = 38000.7 m³