If x = 10 cm, y = 6 cm, and z = 16 cm, what is the surface area of the geometric shape formed by this net? A. 752 cm2 B. 632 cm2 C. 512 cm2 D. 572 cm2

1 answer

To calculate the surface area of a geometric shape formed by specific dimensions, we need to determine what type of shape the net represents. However, since it's not specified whether this is a rectangular prism (cuboid), a triangular prism, or another shape, I'll assume it is a rectangular prism for the purpose of this calculation, as that is a common type of geometric shape with three dimensions.

For a rectangular prism with dimensions \(x\), \(y\), and \(z\):

  • Length (l) = x = 10 cm
  • Width (w) = y = 6 cm
  • Height (h) = z = 16 cm

The formula for the surface area \(A\) of a rectangular prism is:

\[ A = 2(lw + lh + wh) \]

Now substituting the values into the formula:

  1. Calculate each area component:

    • \(lw = 10 , \text{cm} \times 6 , \text{cm} = 60 , \text{cm}^2\)
    • \(lh = 10 , \text{cm} \times 16 , \text{cm} = 160 , \text{cm}^2\)
    • \(wh = 6 , \text{cm} \times 16 , \text{cm} = 96 , \text{cm}^2\)
  2. Now sum these areas:

    • \(lw + lh + wh = 60 + 160 + 96 = 316 , \text{cm}^2\)
  3. Finally, multiply by 2 to find the total surface area:

    • \(A = 2 \times 316 = 632 , \text{cm}^2\)

Thus, the surface area of the geometric shape is 632 cm².

The correct answer is B. 632 cm².