A right circular hollow cylinder of internal volume 540 cm3...............?

Question

1. A right circular hollow cylinder of internal volume 540 cm3 and internal base radius 3 cm, contains water of volume 162 cm3. A cuboid having square base area 9 cm2 and height 10 cm is placed into the cylinder, with its square base resting completely on the base of the cylinder. What is the increase in the height of water? (Take π (pi) as 3, Ignore the width of the cylinder)

Answer 1

the water tends to raise till the volume of water displaced is equal to volume of the cuboid

before the cuboid is placed height of water is 162/(3*3^2)=6cm

the space left after placing the cuboid (upto the height 10cm)=[(3*3^2)-9]*10= 18*10=  180 cm3

from above value we can conclude that water is confined to the spaces between walls of cylinder and the cuboid

for 162 cm3 from the available space the height reached is 162/18=9cm

hence height of water increasesby 9-6=3 cm  

Answer 2

since the height of the cube is 10 cm and the height of the water which is already in the cylinder is only 6 cm, then the volume of the water which will be displaced would only be equal to:

height of cube dipped in water x square base

6(9) = 54 cm3

The area which can now be occupied by the water once the cube is submerged is equal to:

base area of cylinder - base area of cube

3(9) - 9 = 18 cm2

just plug in the added volume, to the V = pi r2 h equation and you'll get the increase in height,

54 = 18 h

h = 3

make sure you replace pi r2 with 18cm2

3cm is increase in height

Answer 3

height of water level = 8.9126768 cm

Solution :

Volume of the cuboid = height * area = 10 * 9 = 90 cm3

Now, the water will raise as you dip the cuboid, now dipped completely and measure the volume occupied by water now.

It will be 162 + 90 = 252 cm3 = height of water level * area of base

= height of water level * π * 3 * 3 = 252

=>height of water level = 8.9126768 cm.

Answer 4

First, find the current height of the water:

Volume = (height)(radius^2)(pi)

162 = (height)(3^2)(pi)

height = 162 / 9pi

Now....

Volume of cuboid

= (area of base)(height)

= (9)(10)

= 90 cm^3

So, the volume in the cylinder

= (water) + (volume of cuboid)

= 162 + 90

= 252 cm^3

The water (+ cuboid) forms a solid cylinder with the same base as the cylinder it's in.

Volume of water cylinder = (height)(radius^2)(pi)

252 = h(3^2)(pi)

h = 252 / 9pi

To find the increase in the height of the water.....

(height after adding cuboid) - (original height)

= (252 / 9pi) - (162 / 9pi)

= 90 / 9pi

= 10 / pi