Question

a tent is in the form of a cone mounted on a cylinder. The radius and height of the cylinder and 16m and 30m respectively. The height of the cone is 12m . Find the area of the canvas required.​

Answer 1

Answer

Given :-

A tent in the form of a cone mounted on a cylinder.

The radius, r and height, H of the cylinder are 16 m and 30 m respectively.

The radius and height of the cone are 16 m and 12 m respectively.

To Find :-

Area of the canvas required.

Solution :-

The canvas will be required to cover the cone and cylinder, which means we will have to find the curved surface of cone and cylinder and then add them to get the required canvas.

We have,

Radius, r = 16 m

Height, H = 30 m

So,

⇒ C.S.A of Cylinder = 2πrH

⇒ C.S.A of Cylinder = 2×π×16×30

⇒ C.S.A of Cylinder = 960π m²

Further, The area of canvas required is,

⇒ CSA of Cone + CSA of Cylinder

⇒ 320π + 960π

⇒ 1280π m²

Hence, The area of canvas required

is 1280π m²

Answer 2

Given :-

• A tent in the form of a cone mounted on a cylinder.

• The radius, r and height, H of the cylinder are 16 m and 30 m respectively.

• The radius and height of the cone are 16 m and 12 m respectively.

To Find :-

• Area of the canvas required.

Solution :-

The canvas will be required to cover the cone and cylinder, which means we will have to find the curved surface of cone and cylinder and then add them to get the required canvas.

Curved Surface Area of Cone,

We have,

• Radius, r = 16 m
• Height, h = 12 m

So,

• C.S.A of Cone = πrl
• C.S.A of Cone = πr√(h² + r²)
• C.S.A of Cone = π × 16 × √( 144 + 256 )
• C.S.A of Cone = 16π√400
• C.S.A of Cone = 320π m²

Similarly, Let us find the Curved Surface Area of cylinder,

We have,

• Radius, r = 16 m
• Height, H = 30 m

So,

• C.S.A of Cylinder = 2πrH
• C.S.A of Cylinder = 2×π×16×30
• C.S.A of Cylinder = 960π m²

Further, The area of canvas required is,

• CSA of Cone + CSA of Cylinder
• 320π + 960π
• 1280π m²

Hence, The area of canvas required is 1280π m²

 

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