Question

Two solid spheres made of the same metal weights 1500 grams and 96 grams if the diameter of the smaller sphere is 12 cm, find the diameter of the sphere

Answer 1

Since the spheres are made of same material, ratio of volume = ratio of weight
$if \: r1 \: \: and \: \: r2 \: are \: the \: radius \\ ratio \: of \: volmes = \\ {( \frac{r1}{r2} )}^{3} = \frac{1500}{96} = 15.625$
$\frac{r1}{r2} = 2.5 \\ given \: r2 = \frac{12}{2} = 6\\ r1 = 2.5 \times 6= 15$
Thus diameter of larger sphere = 30 cm