Question

Two spheres of same metal weight 1kg and 7kg. The radius are 3cm and 8cm. Then both the spheres are melted to form a single big sphere. Find the volume and surface area of the new sphere.

Answer 1

Solution:
Volume of 1st sphere = 4/3 π r^3
= 4/3 × π × 3^3
= 4 × π × 9
= 36π cm^3

Volume of 2nd sphere
= 4/3 × π × 8^3
= 2048/3 π cm^3

Now volume of new sphere is to be equal to volume of 1st sphere plus volume of 2nd sphere, as both spheres are melted to form the new sphere.

Volume of new sphere,
4/3 π R^3 = 36π + (2048/3 π)
π × R^3 = (108π + 2048π)/3 × 4/3
π × R^3 = 2156π/4
Therefore, R^3 = 539
R = 8.13 cm

Therefore, volume of new sphere = 4/3 πR^3
= 4/3 π × 8.13^3
= 2250.92 cm^3

& Surface area of new sphere = 4πR^2
= 4π × 8.13^2
= 830.60 cm^2

Hence, the volume of new sphere is 2250.92 cm^3 & its surface area is 830.60 cm^2