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  • Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm.

Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm.

Answers (1)

Answer 150

Solution

           Given:- Diameter of marble = 1.4 cm

                       Diameter of beaker = 7cm

            Diameter of marble = 1.4 cm

      \text{ Radius of marble}=\frac{1.4}{2}=0.7 cm

            The volume of 1 marble

=\frac{4}{3} \pi r^3=\frac{4}{3}\pi (0.7)^3

=\frac{4}{3} \times 3.14 \times 0.343=1.43cm^3

            Diameter of beaker = 7 cm

         \text{ Radius of beaker}=\frac{7}{2}=3.5 cm

            Water level rises(h) = 5.6cm

            Volume of water

=\pi r^2 h=(3.14)(3.5)^2(5.6)

                        =215.40

          \text{ Number of marbles required}=\frac{\text {volume of water }}{\text {volume of 1 marble }}

                        =\frac{215.40}{1.43}=150

Hence 150 marbles should be dropped into the beaker.

So that the water level rises by 5.6 cm.

Posted by

infoexpert21

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