A toy is in the form of a cone of radius 3.5m mounted on a hemisphere of same radius, the total height of a toy is 15.5cm. find the S.A of t

Question

A toy is in the form of a cone of radius 3.5m mounted on a hemisphere of same radius, the total height of a toy is 15.5cm. find the S.A of the toy. ​

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Josie 1 month 2021-08-20T04:26:03+00:00 2 Answers 0 views 0

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    0
    2021-08-20T04:27:49+00:00

    GIVEN :

    • A toy is in the form of a cone of radius 3.5m mounted on a hemisphere of same radius, the total height of a toy is 15.5 cm.

    TO FIND :

    • The total surface area of the toy = ?

    SOLUTION :

    Let the radius, height and slant height of the cone be the r cm, h cm and l cm respectively.

    r = 3.5 cm

    h = ( 15.5 – 3.5 ) = 12 cm

    ➨ l = \sf \sqrt{(3.5)^{2} + (12)^{2}}

    ➨ l = \sf \sqrt{12.25 + 144}

    ➨ l = \sf \sqrt{156.25}

    \pink{\sf l =12.5 \:cm}

    So,

    ➨ TSA of the toy = 2πr² + πrl

    ➨ TSA of the toy = 2π(3.5)² + π(3.5)(12.5)

    ➨ TSA of the toy = 24.5π + 43.7π

    ➨ TSA of the toy = 68.25π

    ➨ TSA of the toy = 68.25 × 22/7

    TSA of the toy = 214.5 cm²

    Therefore, TSA of toy is 214.5 cm².

    0
    2021-08-20T04:27:50+00:00

    SOLUTION :-

    Radius of cone = Radius of hemisphere = 3.5cm

    Height of conical part = 15.5 – 3.5 = 12cm

    Slant height = √(r² + h²) = 15/2cm

    Now,

    C.S.A= C.S.A of conical part = C.s.a of hemisphere

    C.S.A = πrl + 2π

    C.S.A = 214.5 cm²

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