A hollow sphere of internal and external radii $6$ cm and $8$ cm respectively is melted and recast into small cones of base radius $2$ cm and height $8$ cm. Find the number of cones.

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Solution

No. of cones = $\frac{V o l u m e o f s p h e r e}{v o l u m e o f 1 c o n e}$

$\frac{\frac{4}{3} π (R^{3} - r^{3})}{\frac{1}{3} π r_{c}^{2} h_{c}} = \frac{4 (8^{3} - 6^{3})}{2 \times 2 \times 8} = 37$ cones

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A hollow sphere of internal and external radii 6cm and 8cm respectively is melted and recast into small cones of base radius 2cm and height 8cm. Find the number of cones.

No. of cones = Volume of spherevolume of 1 cone43π(R3−r3)13πr2chc=4(83−63)2×2×8=37 cones

A hollow sphere of internal and external radii $6$ cm and $8$ cm respectively is melted and recast into small cones of base radius $2$ cm and height $8$ cm. Find the number of cones.

No. of cones = $\frac{V o l u m e o f s p h e r e}{v o l u m e o f 1 c o n e}$

$\frac{\frac{4}{3} π (R^{3} - r^{3})}{\frac{1}{3} π r_{c}^{2} h_{c}} = \frac{4 (8^{3} - 6^{3})}{2 \times 2 \times 8} = 37$ cones