Question

the volume of two spheres are in ratio 64 : 27 find the difference of their surface area if the sum of their radius is 7 cm

Answer 1

volume of sphere is proportional to cube of radius

volume of first sphere: volume of 2nd sphere = 64:27

therefore cube of radius of 1st sphere : cube of radius of 2nd sphere =64 :27

then, radius of 1st sphere / radius of 2nd sphere =
$\sqrt[3]{64} \div \sqrt[3]{27}$
= 4/3

sum of radius = 7 cm

radius of first sphere =7×4÷7 =4 cm
radius of 2nd sphere =7-4=3 Surface area of sphere =
$4\pi {r}^{2}$
difference of surface area = 4 π(square of radius of 1st spher- square of radius of 2nd sphere )
=4π×(16-9)
=4π×7
=28π sq.cm