Question 11 Mark
A spherical metal ball of radius 8cm is melted to make 8 smaller identical balls. The radius of each new ball is _________cm.
Answer
View full question & answer→A spherical metal ball of radius 8cm is melted to make 8 smaller identical balls. The radius of each new ball is 4cm.
Solution:
Let, radius of spherical ball be R = 8,
And radius of 8 identical balls be r,
According to question,
Volume of larger sphere = 8 × volume of 8 identical balls
$\frac{4}{3}\pi\text{R}^3=8\times\frac{4}{3}\pi\text{r}^3$
$(8)^3 = 8 \times \text{r}^3$
$8 \times 8 \times \frac8 8 = \text{r}^3$
$64 = r^3$
$(4)^3 = r^3$
$r = 4cm$
Solution:
Let, radius of spherical ball be R = 8,
And radius of 8 identical balls be r,
According to question,
Volume of larger sphere = 8 × volume of 8 identical balls
$\frac{4}{3}\pi\text{R}^3=8\times\frac{4}{3}\pi\text{r}^3$
$(8)^3 = 8 \times \text{r}^3$
$8 \times 8 \times \frac8 8 = \text{r}^3$
$64 = r^3$
$(4)^3 = r^3$
$r = 4cm$