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Find the volume of a cube whose total surface area is 486 cm square
The Correct answer is 729 cubic centimeters.
Explanation
Relate surface area and side length:
The total surface area of a cube is the sum of the areas of all its six faces.
Each face of a cube is a square with side length equal to the cube’s side length (let’s call it “s”).
Therefore, the area of each face is s².
The total surface area (SA) can be expressed as:
SA = 6 * s²
We are given the total surface area (SA) as 486 cm².
Solve for side length:
Substitute the known value of SA into the equation:
486 cm² = 6 * s²
Divide both sides by 6 to isolate s²:
s² = 81 cm²
Take the square root of both sides to find the side length:
s = √81 cm = 9 cm
Find the volume:
The volume of a cube is calculated by cubing its side length:
Volume = s³
Substitute the value of s you found:
Volume = (9 cm)³
Calculate the volume:
Volume = 729 cm³
Therefore, the volume of the cube is 729 cubic centimeters.
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Source: Math Hello Kitty
Categories: Math
