Question

how many meters of cloth 5 m wide will be required to make a conical tent with base radius 7 and height 24

Answer 1

Given :

• width of cloth , B = 5 m
• Radius of conical tent to be made , r = 7 m
• Height of conical tent , h = 24 m

To find :

• Length of Cloth required to make the tent , L = ?

Formula used :

▶Curved Surface Area of cone

• π r l

( where r is radius and l is slant height of cone )

▶formula for Slant height of cone

• l² = r² + h²

( where l is slant height of cone , r is radius of cone , h is height of cone ; using Pythagoras theorem )

Solution :

Calculating slant height of cone (l)

→ l² = r² + h²

→ l² = (7)² + (24)²

→ l = √(625)

→ l = 25 m

Calculating CSA of cone

→ CSA of cone = π r l

→ CSA of cone = (22/7) × (7) × 25

→ CSA of cone = 550 cm²

Calculating length of 5 m wide cloth

Since , cloth is used to make conical tent , therefore Area of rectangular cloth will be equal CSA of conical tent

so,

→ L × B = CSA of cone

→ L × 5 = 550

→ L = 550 / 5

→ L = 110 m

Therefore,

Length of cloth required will be 110 metres.

Answer 2

Given ,

Width of cloth = 5 m

Radius of conical tent (r) = 7 m

Height of conical tent (h) = 24 m

We know that , the CSA of cone is given by

$\large\boxed{ \sf{CSA \: of \: cone =\pi rl }}$

Where ,

l = slant height = √(r² + h²)

Thus ,

Slant height (l) = √{(7)² + (24)²}

Slant height (l) = √(49 + 576)

Slant height (l) = √625

Slant height (l) = 25

And

CSA of cone = 22/7 × 7 × 25

CSA of cone = 22 × 25

CSA of cone = 550 m²

According to the question ,

Area of cloth = CSA of cone

L × 5 = 550

L = 110 m

$\sf \therefore \underline{110 \: m \: long \: cloth \: is \: required \: to \: make \: conical \: tent }$