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The curved surface area of cone …

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The curved surface area of cone is 550cm²and the height of cone is 24cm. Find volume.

Posted by Nimisha Singhal 8 years, 10 months ago

CBSE > Class 09 > Mathematics

1 answers

Naveen Sharma 8 years, 10 months ago

Let Radius of Cone is r and slant height is l.

height of Cone (h) = 24 cm

CSA of cone = 550 cm²

We know,

$l = \sqrt{r^{2} + h^{2}}$

=> $l = \sqrt{r^{2} + 576} . . . . . . . . . . . . (1)$

Also,

$C S A = π \times r \times l$

=> $550 = \frac{22}{7} \times r \times \sqrt{r^{2} + 576}$

Squaring both side,

=> $302500 = \frac{484 r^{2} (r^{2} + 576)}{49}$

=> $30625 = r^{4} + 576 r^{2}$

=> $r^{4} + 576 r^{2} - 30625 = 0$

Put $r^{2} = t$

=> $t^{2} + 576 t - 30625 = 0$

=> $t^{2} + 625 t - 49 t - 30625 = 0$

=> $t (t + 625) - 49 (t + 625) = 0$

=> $(t + 625) (t - 49) = 0$

=> $t + 625 = 0 o r t - 49 = 0$

=> t = - 625 0r t = 49

=> r² = -625 is not possible so r² = 49

=> r = 7

put in (1), we get

$l = \sqrt{49 + 576}$

=> $l = \sqrt{625}$

=> l = 25

=> $V o l u m e o f C o n e = \frac{1}{3} π r^{2} h$

=> $V o l u m e o f C o n e = \frac{1 \times 22 \times 49 \times 24}{3 \times 7}$

=> Volume = 1232cm³

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