Question

If the radius of the cone is 6 cm and perpendicular height is 8 cm then find the curved surface area of cone.(take pi=3.14) *​

Answer 1

Let the perpendicular height and the slant height of the cone be h cm and I cmrespectively

Radius of the base of cone r=8 cm

Curved surface area of the cone =251.2 cm2

∴πrl=251.2 cm2

⇒3.14×8×I=251.2

⇒l=25.12251.2=10

Now,

r2+h2=I2

⇒(8)2+h2=(10)2

⇒64+h2=100

⇒h2=100−64=36

⇒h=36=6 cm

Thus, the slant height and perpendicular height of the cone is 10 cm and 6 cmrespectively.

Answer 2

Height of the cone is not given

Assuming height of the cone =8m

Let radius of base of cone =r

Curved surface area of cone =188.4cm

2

πrl=188.4cm

2

l=

r

2

+h

2

=

r

2

+8

2

=3.14×r×

r

2

+64

=188.4

=r

r

2

+64

=60

Squaring both sides, we get

r

2

(r

2

+64)=3600

r

4

+64r

2

−3600=0

r

4

+100r

2

−36r

2

−3600=0

(r

2

+100)(r

2

−36)=0

r

2

−36=0

r

2

=36

r=6 m