Question

How many metres of cloth of 5 m wide will be required to make a conical tent, the radius of whose base is 7 m and whose height is 24 m? (Take π = 22/7)

Answer 1

Given:

• Radius of base r = 7 m
• Height h = 24 m
• Width of cloth w = 5 m
• Take π = 22/7

Slant height: l = `sqrt(r^2 + h^2)`

Curved (lateral) surface area of cone: A = π r l

Length of cloth required: length = Area/width

Step-wise solution

Compute slant height:

`l = sqrt(r^2 + h^2)`

= `sqrt(7^2 + 24^2)`

= `sqrt(49 + 576)`

= `sqrt625`

= 25 m.

Compute curved surface area (area of cloth needed):

A = πrl = `sqrt(22/7) × 7 × 25` 

= 22 × 25

= 550 m²

Compute the length of cloth of width 5 m:

length = `A/w = 550/5`

= 110 m.