Question

Marbles of diameter 1.4 cm are dropped into a beaker containing some water and fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if water rises by 5.6 cm.

Answer 1

Diameter of marble $=1.4cm$

Therefore,

radius of marble $=\frac{1.4}{2}=0.7cm$

Volume of $1$ marble $=\frac{4}{3}\pi r^3=\frac{4}{3}\times \pi \times {\left(0.7\right)}^3.....\left(1\right)$

Now,

Diameter of beaker $=7cm$

Therefore,

radius of beaker $=\frac{7}{2}=3.5cm$

Height of water $=5.6cm$

Volume of water $=\pi r^{2}h=\pi \times {\left(3.5\right)}^2\times 5.6.....\left(2\right)$

Now,

No. of marbles dropped $=\frac{\text{Volume of water}}{\text{Volume of}1\text{marble}}$

$\Rightarrow$ No. of marbles dropped $=\frac{\pi \times {\left(3.5\right)}^2\times 5.6}{\frac{4}{3}\times \pi \times {\left(0.7\right)}^3}$

$\Rightarrow$ No. of marbles dropped $=150$

Hence $150$ marbles have been dropped in the beaker.