Question

1)A cylindrical container has a diameter of 14cm and a height of 20cm and is full of water. A student pours the water into another cylinder of diameter 20cm. How deep is the water in the second cylinder?

2)A cylindrical water tank is 70cm in diameter. To begin with, it is full of water. A leak starts at the bottom so that it loses 10l of water every hour. How long will it take for the water level to fall by 20cm?

3) A cylindrical storage vessel is 4m in diameter and 31/2m deep. How many kilolitres will it hold?​

Answer 1

1) 9.8 cm

3) 194.68 kilo litters

Step By Step Explanation

Sister these questions are related to volume of cylinder.

You need to use this formula πr²h [ Where r is radius and h is height or depth]

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3)

Given:

Diameter = 4m

Therefore radius = 2m

Depth is 31/2 m

To Find:

How many kilo litters will it hold ?

Actually It's asking about Volume.

Solution:

You know, volume = πr²h

`= \pi {(2 \: m)}^(2) * ( (31)/(2))m`

`= 3.14 * 4 \: {m}^(2) * (31)/(2) m`

`= \: 62 * 3.14 * {m}^(3) \sf [\because \: {m}^(3) = kilolitters]`

`= \sf 194.68 \: \: kilolitters`

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1)

Given:

Diameter = 14 cm

`\sf \therefore \: radius \: = 7 \: cm`

height = 20 cm

Diameter of other cylinder = 20 cm

`\sf \therefore \: radius = 10 \: cm`

To Find:

Deep of water in other cylinder

Consider the depth of water be x

Solution:

Volume of water will remain constant in both

So,

`V_1 = V_2`

`\sf \: \pi {(r_1)}^(2) h_1 = \pi {( r_2 )}^(2) h_2`

[Eliminating π from both sides]

`{(7)}^(2) * 20= {(10)}^(2)x`

`49 * 20 = 100x`

`x = (49 * 2)/(10)`

`x = (98)/(10) \implies \: 9.8`

Therefore the required value of x is 9.8 cm .