One face of a cube has an area of 121 square inches. What is the volume of the cube?Immersive Reader
Answers
The volume V of a cube is given by the formula: V = e³, where e is the length of one of the 12 congruent edges of the cube, that is, all 12 edges of a cube have the same length. An edge of a cube is the intersection of two of the faces of the cube.
Since we know that the volume of the given cube is 1331 cm³, we can substitute into the volume formula as follows to find e:
V = e³
1331 cm³ = e³
Now, taking the cube root of both sides, we get:
³√(1331 cm³) = ³√(e³)
11 cm = e
Since the length of an edge e of a cube is also the length s of one of the sides a face, which is a square, then we can find the area A of one of the six congruent faces of the given cube is by using the formula A = s², which is the same formula for finding the area of a square. Substituting into this formula, we get:
A = s²
= (11 cm)²
= (11 cm)(11 cm)
= 121 cm² is the area of one of the six (6) congruent faces of the given cube.
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