The surface area of each face .of cube is (x²+4x+4)cm² ..find the length and volume of a cube
Answers
Step-by-step explanation:
the surface area of each face of cube =
(x square + 4x + 4)cm square
= (x square +2x+2x+4)
=x(x+2) + 2(x+2)
= (x+2)(x+2) cm square
the length of each edge of cube=(x+2) cm
the volume of cube =(side) cube
= (x+2)cube
=x cube + 2 cube +6x(x+2)
=x cube +8 +6x square +12x
x cube +6x square + 12x + 8
Answer:
(i)
(ii)
Step-by-step explanation:
(i) Each face of a cube is a square.
So, SA of square = area of square = a² where a is its side.
Thus, a² = x² + 4x + 4
Factorizing x² + 4x + 4,
=> x² + 4x + 4
=> x² + 2x + 2x + 4
=> x(x + 2) + 2(x + 2)
=> (x + 2)(x + 2) => (x + 2)²
As x² + 4x + 4 = (x + 2)² = a²
∴ a = √(x + 2)² => (x + 2) units is the length of square, and thus, the side of cube.
(ii) Volume of cube = a³ where a is its side
Now, a = (x + 2)
So, volume of cube = (x + 2)³
=> x³ + 2³ + 3(x)(2)(x + 2) [Using (a + b)³ identity]
=> x³ + 8 + 6x(x + 2)
=> x³ + 8 + 6x² + 12x
=> (x³ + 6x² + 12x + 8) unit³ is the volume of this particular cube.