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A cylindrical cistern of radius 42 cm is partly filled with water. If a rectangular block measuring 24 cm × 21 cm × 11 cm is wholly immersed in the water, by how much will the water level rise?
- a)1 cm
- b)1.5 cm
- c)1.75 cm
- d)2 cm
Correct answer is option 'A'. Can you explain this answer?
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A cylindrical cistern of radius 42 cm is partly filled with water. If ...
To solve this problem, we need to find the volume of the rectangular block and compare it to the volume of the cylindrical cistern.
The volume of a rectangular block is given by the formula:
Volume = Length x Width x Height
In this case, the length is 24 cm, the width is 15 cm, and the height is 18 cm.
Volume of the rectangular block = 24 cm x 15 cm x 18 cm = 6480 cm^3
The volume of a cylindrical cistern is given by the formula:
Volume = π x radius^2 x height
In this case, the radius is 42 cm and the height is unknown.
We need to determine the height of the cylindrical cistern that corresponds to the volume of the rectangular block.
6480 cm^3 = π x (42 cm)^2 x height
Rearranging the equation, we have:
height = 6480 cm^3 / (π x (42 cm)^2)
height ≈ 6480 cm^3 / (π x 1764 cm^2)
height ≈ 6480 cm^3 / 5541.769 cm^2
height ≈ 1.169 cm
Therefore, the height of the cylindrical cistern that corresponds to the volume of the rectangular block is approximately 1.169 cm.
The volume of a rectangular block is given by the formula:
Volume = Length x Width x Height
In this case, the length is 24 cm, the width is 15 cm, and the height is 18 cm.
Volume of the rectangular block = 24 cm x 15 cm x 18 cm = 6480 cm^3
The volume of a cylindrical cistern is given by the formula:
Volume = π x radius^2 x height
In this case, the radius is 42 cm and the height is unknown.
We need to determine the height of the cylindrical cistern that corresponds to the volume of the rectangular block.
6480 cm^3 = π x (42 cm)^2 x height
Rearranging the equation, we have:
height = 6480 cm^3 / (π x (42 cm)^2)
height ≈ 6480 cm^3 / (π x 1764 cm^2)
height ≈ 6480 cm^3 / 5541.769 cm^2
height ≈ 1.169 cm
Therefore, the height of the cylindrical cistern that corresponds to the volume of the rectangular block is approximately 1.169 cm.
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A cylindrical cistern of radius 42 cm is partly filled with water. If a rectangular block measuring 24 cm × 21 cm × 11 cm is wholly immersed in the water, by how much will the water level rise?a)1 cmb)1.5 cmc)1.75 cmd)2 cmCorrect answer is option 'A'. Can you explain this answer?
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