THE SURFACE AREA OF A SPHERE OF RADIUS 5CM IS 5 TIMES THE AREA OF C.S.AREA OF A CONE OF RADIUS 4CM FIND THE HEIGHT AND VOLUME OF THE CONE .\
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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 × l = 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
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 × l = 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
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