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Cupper sphere of r. 3cm is …

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Cupper sphere of r. 3cm is melted and recast into right circular cones of h.3cm . Find the r of the base of the cone

Posted by Rasmita Behera 6 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Rajan Kumar Pasi 6 years, 7 months ago

Your visualization power is low.
In recasting process, the total volume of first solid shape is used to make another shape(s),
Thus, the volume of first solid = the volume of another solid(s).
Solution: For sphere: let the radius = r cm ; The volume = v cm³

For cone: let the radius = R cm ; The volume = V cm³

	The volume of the sphere (v)= {tex}\large\frac{4\pi r^3}{3}{/tex}{tex}\large\implies\frac{4\pi \times3^3}{3}{/tex}{tex}\large\implies{4\pi 3^2}{/tex}{tex}\large\implies{4\pi \times9}{/tex}{tex}\large\implies\boxed {36\pi}{/tex}
	The volume of the cone (V)= {tex}\large\frac{\pi (R)^2h}{3}{/tex}{tex}\large\implies\frac{\pi \times R^2\times3}{3}{/tex}{tex}\large\implies\boxed{\pi\times R^2}{/tex}
Therefore,	{tex}\large\implies V=v\\ \large\implies {\pi\times R^2} = 36\pi\\(\pi \space of \space both \space sides\space are\space cancelled\space or \space divided)\\ \large\implies { R^2} = 36\space\space\space;\large\implies R=\sqrt{36}\\\large\implies R=6\space cm. {/tex}

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