Question

A CONE IS IN SLANT HEIGHT 25 CM HAS A CSA 550 CM^2 FIND THE HEIGHT OF CONE AND ITS VOLUME.

Answer 1

Answer:

Radius = 7 cm

Volume = 1232 $cm^{3}$   

Step-by-step explanation:

Slant height, l = 25 cm

C.S.A. of cone = 550 $cm^{2}$

Now,

We know,

C.S.A. of cone = $\pi rl$

Now,

⇒ $\pi rl$ = 550 $cm^{2}$

⇒ $\frac{22}{7}$ × r × 25 = 550

⇒ r = $\frac{550 × 7}{22 × 25}$

⇒ r = 7 cm

Now,

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

or,

$h^{2}$ = $l^{2}$ - $r^{2}$

h = $\sqrt{l^{2} -  r^{2} }$

h = $\sqrt{25^{2} - 7^{2} }$

h = $\sqrt{625 - 49}$

h = $\sqrt{576}$

h = 24 cm

So,

Volume of a cone = $\frac{1}{3}$ $\pi$ $r^{2}$ h $cm^{3}$  

                              =  $\frac{1}{3}$ × $\frac{22}{7}$ × 24 × $7^{2}$ $cm^{3}$  

                              = $\frac{1}{3}$ × $\frac{22}{7}$ × 24 × 7 × 7 $cm^{3}$  

                              =  $\frac{1}{3}$ × 22 × 24 × 7 $cm^{3}$  

                              = 1 × 22 × 8 × 7 $cm^{3}$  

                              = 22 × 56 $cm^{3}$  

                              = 1232 $cm^{3}$