Question

the radius and slant height of a cone are in the ratio 3 5 and its curved surface area is 422 3.9 CM square find the volume of a cone Pi is equal to 3.14​

Answer 1

Answer:

Volume of Cone is 27468.72 cm²

Step-by-step explanation:

Given: Ratio of radius, r and slant height, l of come = 3 : 5

           Curved Surface Area = 423.9 cm²

           value of $\pi=3.14$

To find: Volume of cone

Let slant height = 5x and radius = 3x

According to the question,

$\pi rl=423.9$

$3.14\times3x\times5x=423.9$

$47.1x=423.9$

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

$x=9$

⇒ Radius, r = 3 × 9 = 27 cm

    Slant height, l = 5 × 9 = 45 cm

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