Two right circular cones of equal height of radii of base

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Two right circular cones of equal height of radii of base 3 cm and 4 cm are melted together and made to a solid sphere of radius 5 cm. The height of a cone is

1. 10 cm
2. 20 cm
3. 30 cm
4. 40 cm

Correct Option: D

Volume of cone = Volume of sphere

⇒	1	πr₁²h +	1	πr₂²h =	4	πr³
	3		3		3

⇒(r₁² + r₂²)h = 4r³
⇒ (9 + 16)h = 4 × 53
⇒ 25h = 4 × 125
⇒ h = 4 × 5 = 20 cm