Question

Meera is dropping marbles of diameter 1.4 cm into a cylindrical beaker of radius 7 cm containing some water.How many marbles must be dropped by her so that the water in the beaker rises by 28 cm?

Answer 1

Step-by-step explanation:

r1=0.7cm

r2=7cm

h=28cm

v of cylinder

π*49*28=4312cm^3

v of marbles

4πr^3

4π*0.7*0.7*0.7=4.31cm^3

no. of marbles =4312/4.31=1000 marbles approx

Answer 2

3000 marbles are dropped by Meera.

Step-by-step explanation:

diameter of the spherical marbles = 1.4 cm

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

volume of the marble =$\frac{4}{3}\pi r^3$

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

radius of the cylindrical beaker = 7 cm

the water level rises by 28 cm

so, height of the cylindrical beaker = 28 cm

volume of the cylindrical beaker = $\pi r^2h$

= $\pi (7)^2(28)$

let the number of marbles dropped in the beaker = n

then,

n = $\frac{volume of cylinder}{volume of marble}$

n= $\frac{\pi \times 7\times7\times28\times3}{4\times0.7\times0.7\times0.7\times \pi }$

n= $\frac{4116}{1.372}$

n= 3000

hence,

3000 marbles are dropped by Meera.

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