Question

A solid right circular cone of diameter 14cm and the height 8cm is melted to form a hollow sphere. If the external diameter of the sphere is 10cm, find the internal diameter of the s

Answer 1

so the diameter is 6 cm...
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Answer 2

Answer: Internal diameter of sphere is 3 × 2 =6 cm.

Step-by-step explanation:

Since we have given that

Diameter of cone = 14 cm

Radius of cone = 7 cm

Height of cone = 8 cm

So, Volume of cone is given by

$\dfrac{1}{3}\times \pi \times 7\times 7\times 8$

Since it is melted in a hollow sphere,

External diameter of sphere = 10 cm

External radius of sphere = 5 cm

Let the internal radius of sphere be 'r'.

So, Volume of hollow sphere is given by

$\frac{4}{3}\times \pi \times (5^3-r^3)$

Since their volume must be equal.

According to question, it becomes,

$\dfrac{1}{3}\times \pi \times 7\times 7\times 8=\frac{4}{3}\times \pi \times (125-r^3)\\\\392=4(125-r^2)\\\\392=500-4r^3\\\\392-500=-4r^3\\\\-108=-4r^3\\\\\dfrac{108}{4}=r^3=27\\\\r=3$

Hence, Internal diameter of sphere is 3 × 2 =6 cm.