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

Question

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

Piyush Jain · Accepted Answer

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=43πR3⇒r13+r23+r33=R3⇒(1)3+(6)3+(8)3=R3⇒R3=729⇒R=9

Thus, the radius of new sphere=9 cm