Question

A sphere of dia diameter 12.6 CM is melted and cast into a right circular cone of height 25.2 CM find the diameter of the base of the cone

Answer 1

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Answer 2

Answer:

12.6cm

Step-by-step explanation:

Diameter of sphere = 12.6 cm

Radius =$\frac{Diameter}{2} =\frac{12.6}{2}=6.3 cm$

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

So, volume of given sphere =  $\frac{4}{3} \pi \times (6.3)^3$

                                              =  $\frac{4}{3} \pi \times 250.047$

Now Volume of cone = $\frac{1}{3} \pi r^2 \times h$

Since we are given that the height of cone = 25.2 cm

So, volume of given cone = $\frac{1}{3} \pi r^2 \times 25.2$

Since we are given that the sphere in melted into cone

So, volume will remain same

⇒$\frac{4}{3} \pi \times 250.047=\frac{1}{3} \pi r^2 \times 25.2$

⇒$4 \times 250.047= r^2 \times 25.2$

⇒$1000.188= r^2 \times 25.2$

⇒$\frac{1000.188}{25.2} = r^2$

⇒$39.69= r^2$

⇒$\sqrt{39.69}= r$

⇒$6.3= r$

Thus the radius of cone is 6.3 cm

Diameter = radius *2 = 6.3*2 = 12.6 cm

Hence the diameter of cone is 12.6 cm.