Question

The cost of painting the total surface area of a cone at 25 paise per square CM is Rs176.find the volume of the cone. if it's slant height is 25cm.

Answer 1

• The total surface area of cone = 17600/25 cm²

   ⇒  πr(r+l) = 704    [ l = 25 cm]

   ⇒  πr ( r+ 25) = 704

   ⇒ πr² + 25πr = 704

    ⇒  π(r²+25 r) = 704

    ⇒ r² + 25 r = 704/π

   ⇒ r² + 25 r - 224 = 0

    ⇒ r² + 32 r - 7 r - 224 = 0

   ⇒ r(r+32) - 7(r+ 32) = 0

   ⇒ (r-7)(r+32)= 0

So, r = 7 or -32

-32 can't possible.

So

r = 7 cm

• Volume of  cone = 1/3 πr²h

where h = √l² - r² = √25²-7² = √625-49 =  √576 = 24 cm

• Volume = 1/3 x 22/7 x 7 x 7 x 24

                        =25872/21 = 1232 cm³

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