Question

A cone of height 8 m has a curved surface area 188.4 m2. Find its volume. [π = 3.14]

Answer 1

Answer:

Volume = 301.44 m^3

Step-by-step explanation:

CSA = 188.4

188.4 = pi*r*l

188.4/3.14 = r*root(r^2 + h^2)

60 = r*root (r^2 + 64)

squaring both sides

3600 = r^2 *(r^2+64)

3600 = r^4 + 64r^2

solving it

((r^4) +  2^6*r^2) -  3600  = 0

solving this as quadratic equation where r^2 =x  (i found out r after doing a very complex method that is not required you can just find r^2 and use it)

you get r = 6, -6 , 10i , -10 i

since r is real and positive

r = 6cm

Volume = pi* r^2 * h /3

Volume =3.14* 36* 8/3

Volume = 3.14*12*8

Volume = 301.44 m^3

Answer 2

Given :-

• Height of cone (h) → 8m
• Curved surface area of cone (C.S.A) → 188.4m²

To Find :-

• Volume of cone (v) → ?

Solution :-

C.S.A → 2πrh = 188.4m²

=> 2 × 3.14 × r × 8 = 188.4

=> 6.28 × r × 8 = 188.4

=> 50.24 × r = 188.4

=> r = 3.75m

Now

Volume → πr²h

=> 3.14 × (3.75)² × 8

=> 3.14 × 14.0625 × 8

=> 353.25m³

Hence,The volume is 353.25m³