Question

A circus tent is in the form of a cone of height 15 m and diameter 16 m.Find the length of Canvas required to make tent if its width is 2 metres.

Answer 1

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Here's your Answer...

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Given;

Diameter = 16m

Radius = 8m

Height = 15m

Curved Surface Area of Cone = pie × r × l ----(1)

For Slant Height l

By Pythagoras thm,

l^2 = r^2 + h^2

=> l^2 = 64 + 225

=> l^2 = 289

=> l = 17m.

Putting l = 17m in equation 1.

=> 3.14 × 8 × 17

=> 427.02m^2.

Breadth = 2m.

Now, L × b = 427

=> l = 427/2

=> length = 213.52m
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Answer 2

The length of Canvas required to make tent if its width is 2 metres is 213.71 m.

Given:

Diameter of a cone ,d = 16 m

Radius of a cone, r = d/2 = 16/2 = 8m

Height of a cone, h = 15 m

Breadth of a canvas = 2 m

To find :The length of Canvas required to make tent if its width is 2 metres.

Formula used:

• Slant Height,$\bf l^2 = r^2 + h^2$
• Curved Surface Area of Cone = πrl

Solution:

Step1: Find slant height:

Let  Slant Height be l.

$\bf l^2 = r^2 + h^2$

$\bf l^2 = 8^2 +15^2$

$\bf l^2 = 64 + 225$

$\bf l^2 = 289$

l = 17 m

Step 2: Find Curved surface area of the cone :

Curved surface area of the cone = πrl

Curved surface area of the cone = $\bf \frac{22}{7} \times 8 \times 17$

Curved surface area of the cone = $\bf \frac{2992}{7}$

Curved surface area of the cone = 427.42 m²

Step 3: Find the length of Canvas :

Area of canvas = Length  × Breadth

427.42 =  Length  × 2

Length = $\bf \frac{427.42}{2}$

Length of the canvas = 213.71 m

Hence, the length of Canvas required to make tent if its width is 2 metres is 213.71 m.

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