Question

R a sphere of diameter 12.6 and cm is melted and cast into right circular cone of height to 25.2 cm find the radius of the base of the cone

Answer 1

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Answer 2

Answer:

The radius of cone is 6.3 cm.

Step-by-step explanation:

Given that,

Diameter of the sphere is 12.6 cm.

The radius is half of diameter.

Hence, the radius of sphere is given by

$R=\frac{12.6}{2}\\\\R=6.3\text{ cm}$

And the height of the cone is 25.2 cm

Now, it has been given that sphere  is melted and cast into right circular cone.

Thus, the volume remains same.

Therefore, we have

volume of cone = volume of sphere

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

3 and π got cancelled out. Hence, the equation becomes

$r^2 h=R^3\\\\r^2=\frac{4R^3}{h}\\\\r^2=\frac{4\times6.3^3}{25.2}\\\\r^2=\frac{3969}{100}\\\\r=\frac{63}{10}\\\\r=6.3$

The radius of cone is 6.3 cm.