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Question

A cylinder container with diameter 48cm contains sufficient water to submerge a rectangular solid of iron with dimensions 33cm x 18cm x 12cm. Find the rise in the level of water when solid is completely submerged?

Options:
A .  2.94 cm
B .  3.94 cm
C .  4.94 cm
D .  5.94 cm
E .  None of these
Answer: Option B

 -    Diameter of cylinder = 48 cm     
  ⇒ Radius of cylinder (r) = 24 cm
  Now, when the Cuboid  is completely submerged
  Then, Volume of cylindrical portion formed by original water level and after increase in water level =
   volume of cuboid
  ⇒ πr 2 h = 33 cm × 18 cm × 12 cm
  22/7 x 24 x 24 x h = 33 cm × 18 cm × 12 cm
  h = (33 cm × 18 cm × 12 cm x7)/ 22 x 24 x 24=3.94cm
  Hence, the required increase in water level is 3.94 cm


We are given a cylinder container with diameter 48cm which contains sufficient water to submerge a rectangular solid of iron with dimensions 33cm x 18cm x 12cm. We need to find the rise in the level of water when the solid is completely submerged.

Let's first find the volume of the rectangular solid of iron:

Volume of the rectangular solid = Length x Breadth x Height

= 33cm x 18cm x 12cm

= 7128 cubic cm

Now, let's find the volume of water displaced when the solid is completely submerged in the cylinder container. Since the volume of water displaced will be equal to the volume of the solid, we have:

Volume of water displaced = 7128 cubic cm

Let's find the height by which the level of water will rise in the cylinder container:

Volume of water displaced = πr^2h

where r is the radius of the cylinder and h is the height by which the level of water will rise.

Since the diameter of the cylinder is given as 48cm, the radius will be half of it, i.e., r = 24cm.

Substituting the values in the formula above, we get:

7128 = π x 24^2 x h

h = 7128 / (π x 24^2)

h ≈ 3.94 cm

Therefore, the rise in the level of water when the solid is completely submerged is 3.94 cm.

Hence, the correct option is B. 3.94 cm.

If you think the solution is wrong then please provide your own solution below in the comments section .


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