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Marbles of diameter $1.4$ cm are dropped into a beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped init if water rises by $56$ cm?

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56 cm

53 cm

57 cm

59 cm

answer is A.

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Detailed Solution

Given, marbles of diameter 1.4 cm, they are dropped in a beaker containing water and are fully submerged. The diameter of the beaker is 7 cm.
Volume of the cylinder is

π

r^{2} h

, where r and h are the radius and height of the cylinder respectively.
Volume of the sphere is

\frac{4}{3} π r^{3}

, where r is the radius of the sphere.
Marble diameter = 1.4cm.
Radius =

\frac{1.4 cm}{2} = 0.7 cm

.
Radius of the beaker

\frac{Diameter}{2}

= \frac{7}{2}

= 3.5cm.
Water rises level (h )= 56 cm.
Now, volume of water rise in the beaker is,

\Rightarrow π \times {3.5 cm}^{2} \times 56

\Rightarrow 686 π {cm}^{3}

.
Now, volume of the spherical marble is,

\Rightarrow \frac{4}{3} \times π \times {(0.7)}^{3}

\Rightarrow \frac{1.372}{3} πc m^{3}

.
Finding the number of marbles dropped.

Number of marbles dropped = \frac{volume of water rise}{volume of marbel}

\Rightarrow \frac{686 π}{\frac{1.372}{3} π}

\Rightarrow 1500

.
Thus,

1500

marbles have been dropped in the beaker if water rises by

56 cm .

Hence, option 1 is correct.

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