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Answer:

1. Formula of Surface of cube

A = 6a²

but, we need to find the length of the each edge of the cube, therefore the formula is:

A = √A/6

A = √A/6

= √486cm²/6

= √486cm²/6 ÷ 6/6

= √81cm²

A = 9cm

therefore, the length of each side of the cube is 9cm

2. Formula of Surface of the cube:

A = 6a²

A = 6a²

= 6(6cm)²

= 6(36cm²)

A = 216cm²

therefore, the surface area of cube is 216cm².

3. Formula of Rectangular Prism:

A = 2(lw + lh + wh)

first, we convert m to cm before we compute the surface area of the rectangular prism

3m = ____ cm

1m = 100cm

3 × 100

= 300cm

2m = ____ cm

1m = 100cm

2 × 100

= 200cm

Now, we compute the surface area of the rectangular prism

A = 2(lw + lh + wh)

= 2((8cm)(300cm) + (8cm)(200cm) + (300cm)(200cm))

= 2(2,400cm² + 1,600cm² + 60,000cm²)

= 2(64,000cm²)

A = 128,000cm²

therefore, the surface area of rectangular prism is 128,000cm².

4. Formula of surface area of cylinder

A = 2πd/2 × h + 2π × (d/2)²

A = 2πd/2 × h + 2π × (d/2)²

= 2(3.14)(12cm/2)(11cm) + 2(3.14)(12cm/2)²

= 2(3.14)(6cm)(11cm) + 2(3.14)(6cm)²

= 2(3.14)(66cm²) + 2(3.14)(36cm²)

= 2(207.24cm²) + 2(113.04cm²)

= 414.48cm² + 226.08cm²

A = 640.56cm²

therefore, 640.56cm² needed to cover the box.