Question

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

Answer 1

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**.