A solid sphere of radius ‘r’ is melted and cast into the shape of

1.	A solid sphere of radius ‘r’ is melted and cast into the shape of a solid cone of height ‘r’. The radius of the base of the cone isA) 2r B) 3r C) 4r D) 6r
Answer» Correct option is: A) 2r Let radius of the base of the cone be R. \(\because\) Volume of cone = volume of sphere = \(\frac 13 \pi R^2 h\) = \(\frac 43 \pi r^3 h\) = \(R^2 = \frac {4r^3}{h}\) = \(R^2 = \frac {4r^3}{r}\)( \(\because\) h = r) = \(4r^2\) = \((2r)^2\) \(\therefore\) R = 2r Hence, the radius of the base of the cone is 2r. Correct option is: A) 2r

A solid sphere of radius ‘r’ is melted and cast into the shape of a solid cone of height ‘r’. The radius of the base of the cone isA) 2r B) 3r C) 4r D) 6r

Answer»

Correct option is: A) 2r

Let radius of the base of the cone be R.

\(\because\) Volume of cone = volume of sphere

= \(\frac 13 \pi R^2 h\) = \(\frac 43 \pi r^3 h\)

= \(R^2 = \frac {4r^3}{h}\)

= \(R^2 = \frac {4r^3}{r}\)( \(\because\) h = r)

= \(4r^2\)

= \((2r)^2\)

\(\therefore\) R = 2r

Hence, the radius of the base of the cone is 2r.

Correct option is: A) 2r