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

Question

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

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Eden 1 month 2021-08-12T21:04:26+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-12T21:05:26+00:00

    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 }

    0
    2021-08-12T21:05:32+00:00

    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.

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