If a solid sphere of radius r is melted and cast into the shape of a s

1.	If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is : A. 2r B. 3r C. r D. 4r
Answer» Option : (A) Volume of a sphere = \(\frac{4}{3}\)πr³ Volume of a solid cone = \(\frac{1}{3}\)πr²h Given, solid sphere of radius r is melted and cast into the shape of a solid cone of height r Let the base radius be A. ⇒ \(\frac{4}{3}\)πr³ = \(\frac{1}{3}\)π × A² × r ⇒ A = 2r

If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is : A. 2r B. 3r C. r D. 4r

Answer»

Option : (A)

Volume of a sphere = \(\frac{4}{3}\)πr³

Volume of a solid cone = \(\frac{1}{3}\)πr²h

Given,

solid sphere of radius r is melted and cast into the shape of a solid cone of height r

Let the base radius be A.

⇒ \(\frac{4}{3}\)πr³ = \(\frac{1}{3}\)π × A² × r

⇒ A = 2r