# The surface area of a sphere of radius 5cm is five times the area of the curved surface of a cone of radius 4cm. Find the height and volume of the cone (pi = 22/7)

Let R be the radius of the sphere.

Suppose the radius of cone be r and h respectively.

Surface area of the sphere = 4πR2 = 4π (5 cm)2 = 100π cm2

Curved surface area of cone = πrl = π × 4 cm × = 4πl

Given, Surface area of the sphere = 5 × Curved surface area of the cone

∴ 100π cm2 = 5 × 4π l cm

⇒ 100π cm2 = 20πl cm

⇒ l = 5 cm

Slant height of the cone,

∴ (4 cm)2 + h 2 = (5 cm)2

⇒ h 2 = 25 cm2 – 16 cm2

⇒ h 2 = 9 cm2

⇒ h = 3 cm

Height of the cone, h = 3 cm

∴ Volume of the cone

• 107
50.27 [approx]
• 11
thank u @abhijeet
• -1
thank you

• -4
h-3cm

• -5
And volume will be 5.287 (approximately) right ??
• -1
volume of cone = 1/3 pie r2 h
height = 3 cm
=1/3*22/7*4*4*3
=22/7*4*4   (because 3 and 3 are cut )
=22*4*4/7
=352/7
=50.28 cu.cm

• 5
It can be 49.95also
• 0
Can be 49.95 alsooo
• 0
49.95
• -4
• -2
It is helpful for me to understand
• 0

• 6
after finding height i.e 3cm we get volume of cone= 1/3*22/7*4*4*3 >> 352/7cm*cm*cm

• 5
50.24
• -2
Very tough
• -1
THANK YOU VERY MUCH
SAME QUESTION WAS ASKED IN EXAM