Math Problem Statement

The net of a cuboid is shown. Work out the surface area of the cuboid. The dimensions provided are 5 cm, 3 cm, and 2 cm.

Solution

To calculate the surface area of the cuboid from the provided net, we need to determine the area of each rectangle in the net and then sum them up.

The dimensions of the cuboid are:

  • Length = 5 cm
  • Width = 3 cm
  • Height = 2 cm

The net consists of 6 rectangles:

  1. 2 rectangles with dimensions 5 cm × 3 cm

    • Area of each = 5×3=15cm25 \times 3 = 15 \, \text{cm}^2
    • Total area for these two = 2×15=30cm22 \times 15 = 30 \, \text{cm}^2
  2. 2 rectangles with dimensions 5 cm × 2 cm

    • Area of each = 5×2=10cm25 \times 2 = 10 \, \text{cm}^2
    • Total area for these two = 2×10=20cm22 \times 10 = 20 \, \text{cm}^2
  3. 2 rectangles with dimensions 3 cm × 2 cm

    • Area of each = 3×2=6cm23 \times 2 = 6 \, \text{cm}^2
    • Total area for these two = 2×6=12cm22 \times 6 = 12 \, \text{cm}^2

Now, summing all these areas: 30+20+12=62cm230 + 20 + 12 = 62 \, \text{cm}^2

Thus, the surface area of the cuboid is 62 cm².

Would you like more details or further clarification?

Here are 5 related questions to consider:

  1. How would the surface area change if the dimensions were doubled?
  2. What is the formula for the surface area of a general cuboid?
  3. How would you find the volume of this cuboid?
  4. Can the net of a cuboid be arranged differently while maintaining the same surface area?
  5. How can you distinguish a cube from a cuboid based on the net?

Tip: When calculating surface area from a net, ensure you correctly pair up corresponding faces of the cuboid.

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Math Problem Analysis

Mathematical Concepts

Geometry
Surface Area
Nets of 3D Shapes

Formulas

Surface area of a cuboid = 2(lw + lh + wh)

Theorems

Surface area calculation using nets

Suitable Grade Level

Grades 6-8