Question

the radius and height of a cone are in the ratio 3 :5 and its curved surface area is 423.9cm square. find the volume of the cone
$(\pi = 3.14)$
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Answer 1

let r=3x

h=5x

as l=√r²+h²

=x√34

CSA of cone=πrl=423.9

3.14*3x*x√34=423.9

x²=45/√34

x=7.7

volume of cone=πr²h/3

=3.14*9x²*5x/3

=47.1*x³

=47.1*7.7*7.7*7.7

=21502.7 cm³

Answer 2

Answer:

Cone's volume is 27468.72 cm²

Step-by-step explanation:

Given: Radius : slant height = 3 : 5

           Curved Surface Area of cone = 423.9 cm²

To find: Volume of cone

Let slant height , l = 5x and radius , r = 3x

Now,

$\pi rl=423.9$

$3.14\times3x\times5x=423.9$

$47.1x=423.9$

$x=\frac{423.9}{47.1}$

$x=9$

⇒ r = 3 × 9 = 27 cm

    l = 5 × 9 = 45 cm

Height of cone, h = $\sqrt{l^2-r^2}=\sqrt{(45)^2-(27)^2}$ = 36 cm

Volume of Cone = $\frac{1}{3}\pi r^2h$

                            = $\frac{1}{3}\times3.14\times(27)^2\times(36)$

                            = 27468.72 cm²

Therefore, Volume of Cone is 27468.72 cm²