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 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 is
A) 2r
B) 3r
C) 4r
D) 6r
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2 Answers
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.
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