Question

30 spherical balls of radius 7 cm each are dropped in a cylindrical tank of radius 49 cm. If the tank is already filled up to a height of 207 m, then find the percentage increase in height.​

Answer 1

Answer:

200%

Step-by-step explanation:

Given:

No. of spherical balls = 30

Radius of balls = 7 cm

Radius of cylinder = 49 cm

Filled height of cylinder = 20/7 cm

Find: Percentage increase in height

Solution-

Let increase in height of cylinder is h.

Thus, increased volume of cylinder = pi x r x r x h

= pi x 49 x 49 x h cubic cm ........ (1)

Volume of 30 spherical balls = 30 x 4/3 x pi x 7 x 7 x 7 cubic cm ........ (2)

Equating equations 1 and 2, we get

h = 40 / 7

So percentage increase in height = (40/7) x 100 / (20/7) = 200%

Answer 2

According the question :-

Total number of spherical balls = 30                       (given)

Radius of each ball = 7 cm                                         (given)

Radius of the cylinder = 49 cm                                  (given)

Height of cylinder when it is filled = $\frac{20}{7}$ cm              (given)

Here we have to find the percentage increase in height

Let increase in height of cylinder = L.

Now the increased volume of cylinder will be :-

= pi x r x r x L

= pi x 49 x 49 x L cubic cm ........ (1)

Here the total volume of 30 spherical balls

= 30 x $\frac{4}{3}$ x pi x 7 x 7 x 7 cubic cm ........ (2)

From equations (1) and (2), we get

L = $\frac{40}{7}$

Hence the percentage increase in height will be :-

= ( $\frac{40}{7}$) x 100 ÷ ($\frac{20}{7}$ )

=$\frac{4000}{7}$ ÷ $\frac{20}{7}$

= $\frac{4000}{7}$ ×$\frac{7}{20}$

= $\frac{4000}{20}$

= 200%

∴ the percentage increase in height will be 200%

Ans :-  The percentage increase in height will be 200%

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