A metallic sphere of radius 10.5 cm is melted and thus recast into small cones,

Question:

A metallic sphere of radius 10.5 cm is melted and thus recast into small cones, each of radius 3.5 cm and height 3 cm. Find how many cones are obtained.

Solution:

Given that

Metallic sphere of radius = 10.5 cm

Cone radius = 3.5 cm

Height of radius = 3 cm

Let the number of cones obtained be x

$\mathrm{v}_{\mathrm{s}}=\mathrm{X} \times \mathrm{v}_{\text {cone }}$

$\frac{4}{3} \pi r^{3}=x \times \frac{1}{3} \pi r^{2} h$

$x=\frac{4 \times 10.5 \times 10.5 \times 10.5}{3.5 \times 3.5 \times 3}$

x = 126

Therefore number of cones = 126

 

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