Question

The diameter of a metallic sphere is 4.2 cm It is melted to recast into a right circular cone of height 8.4 cm find the radius of the base?

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

2.1 cm

Step-by-step explanation:

Diameter of metallic sphere is 4.2 cm

Radius = Diameter/2 = 4.2/2 = 2.1 cm

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

                              = $\frac{4}{3} \times 3.14 \times (2.1)^{3}$

                              = $38.77272 cm^3$

Height of cone = 8.4 cm

volume of cone = $\frac{1}{3} \pi r^2 h$

                          = $\frac{1}{3}\times 3.14 \times  r^2 \times 8.4$                

                          = $8.792 \times  r^2$                      

Since we are given that Sphere is melted to recast into cone .

So the volume will be same

So,  $38.77272=8.792 \times  r^2$

 $\frac{38.77272}{8.792}= r^2$

 $4.41= r^2$

 $\sqrt{4.41}= r$

$2.1= r$

Hence the radius of  base is 2.1 cm.