THREE SOLID SPHERES OF IRON HAVING DIAMETER 2CM , 12CM AND 16CM RESPECTIVELY ARE MELTED INTO SPHERE.FIND THE RADIUS OF THE NEW SPHERE

i have read the answer to this question but in the question says the diameters are 2cm. 12cm and 16cm. so the radius will be 1cm, 6cm, 16cm respectively. but when i checked the older answer the radius was taken as 2cm, 12cm, 16cm

Given: Radii r1, r2, r3 of three spheres are 1 cm, 6 cm and 8 cm.

Let radius of new sphere be R.

 

As, we know that,

Also,as three spheres are melted into a single sphere.

∴ Sum of volumes of three spheres = Volume of new sphere
43πr13+43πr23+43πr33=43πR3r13+r23+r33=R3(1)3+(6)3+(8)3=R3R3=729R=9
Thus, the radius of new sphere=9 cm

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