Question

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Spherical Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm., which contains some water. Find the number of marbles that should be dropped in to the beaker, so that water level rises by 5.6 cm.

Answer 1

Formulae used :

$\boxed{\mathbf{Volume \: of \: Cylinder = π{r}^{2}h}}$

$\boxed{\mathbf{Volume \: of \: Sphere = \frac{4}{3}π{r}^{2}}}$

Given,
Diameter of spherical marbles = 1.4cm
Radius = 1.4/2 cm.
Number of marbles = (to be calculated)

Diameter of cylindrical beaker = 7cm.
Radius = 7/2 cm.
Water level (height) = 5.6cm.

$\underline{\underline{\huge\mathfrak{Solution}}}$

Let the number of marbles be x.

Volume of spherical marbles × x = Volume of Cylinder.

$\frac{4}{3} \times \pi \times \frac{1.4}{2} \times \frac{1.4}{2} \times \frac{1.4}{2} \times x = \pi \times \frac{7}{2} \times \frac{7}{2} \times 5.6\\ \\ x = \frac{\pi \times 7 \times 7 \times 5.6 \times 3 \times 2 \times 2 \times 2}{\pi \times 4 \times 1.4 \times 1.4 \times 1.4} \\ \\ x = \frac{49 \times 56 \times 3 \times 8 \times 100}{4 \times 14 \times 14 \times 14} \\ \\ x = \frac{2 \times 3 \times 100}{1} \\ \\ \bf x = 600$

The number of marbles needed to rise the water level by 5.6 cm is 600.