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A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The side of the cube is
The side length of the cube formed when the metal sheet is melted is approximately 6 cm.
To find the side length of the cube formed when the metal sheet is melted, we need to first calculate the volume of the metal sheet and then use that volume to find the side length of the cube.
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The volume of the metal sheet can be calculated using the formula for the volume of a rectangular prism, which is length × width × height.
Given: Length of the metal sheet (l) = 27 cm
Breadth of the metal sheet (b) = 8 cm
Thickness of the metal sheet (h) = 1 cm
Volume of the metal sheet = l × b × h
= 27 cm × 8 cm × 1 cm
= 216 cm³
Now, since the metal sheet is melted into a cube, the volume of the cube will be equal to the volume of the metal sheet.
Volume of the cube = Volume of the metal sheet
Let the side length of the cube be ‘s’.
Volume of the cube = s³
Equating the volumes:
s³ = 216 cm³
To find the side length ‘s’, we take the cube root of both sides:
s = ∛(216 cm³)
Now, calculate the cube root of 216:
s = ∛216 s ≈ 6 cm
So, the side length of the cube formed when the metal sheet is melted is approximately 6 cm.
How to Calculate the Volume of a Cube?
To calculate the volume of a cube, you need to know the length of one of its sides (since all sides of a cube are equal in length). Here’s the formula:
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Volume = side length^3
So, if you have the length of one side (let’s call it “s”), you would calculate the volume by cubing that length:
Volume = s^3
For example, if the side length of the cube is 5 units, then the volume would be:
Volume = 5^3 = 5 × 5 × 5 = 125 cubic units.
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Source: Math Hello Kitty
Categories: Math
