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  • A cone is 8.4\; cm high and the radius of its base is 2.1\; cm. It is melted and recast into a sphere. The radius of the sphere is : (A) 4.2 cm (B) 2.1cm (C) 2.4 cm (D) 1.6 cm

A cone is 8.4\; cm high and the radius of its base is 2.1\; cm. It is melted and recast into a sphere. The radius of the sphere is :

(A) 4.2\; cm

(B) 2.1\; cm

(C) 2.4\; cm

(D) 1.6\; cm

 

Answers (1)

Answer (B)

In the question it i given that the height of cone =8.4\; cm

And, Radius of cone =2.1\; cm

The cone is melted and recast into a sphere

So,

Volume of sphere = Volume of cone

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

(where R is the radius of sphere, r is the radius of cone, h is the height of cone)

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

Putting the given values,

R^{3}=\frac{\left ( 2.1 \right )^{2}\times\left ( 8.4 \right )}{4}=\left ( 2.1 \right )^{2}\times 2.1

R^{3}=\left ( 2.1 \right )^{3}

R=2.1 \; cm

Hence, option (B) is the correct answer.

Posted by

infoexpert23

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