Question

A solid sphere of radius 10.5 cm is melted and recast into smaller solid cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed.
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Answer 1

Step-by-step explanation:

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Answer 2

Therefore the number of cones so formed is 126.

Step-by-step explanation:

Given , A solid sphere of radius 10.5 cm.

Therefore the volume of the sphere = $\frac{4}{3} \pi r^3$

                                                           $=\frac{4}{3} \pi \times 10.5^3$   cm³

The sphere is melted and recast into smaller cones , each of radius 3.5 cm and height 3 cm.

The volume of each cone is $\frac{1}{3} \pi r^2h$

                                             $=\frac{1}{3}\pi\times 3.5^2 \times 3$    cm³

Let the number of cones formed be x

According to the problem,

$\frac{1}{3}\pi\times 3.5^2 \times 3\times x=\frac{4}{3} \pi \times 10.5^3$

$\Leftrightarrow x=\frac{\frac{4}{3} \pi \times 10.5^3}{\frac{1}{3}\pi\times 3.5^2 \times 3}$

$\Leftrightarrow x =126$

Therefore the number of cones so formed is 126.