A net is a two-dimensional layout of all the faces of a three-dimensional solid, arranged so that folding along the edges produces the original solid. Nets reveal the surface area as the sum of flat face areas.
Unfold a 3D solid like a cardboard box—the flat connected pattern you get is a net of that solid.
Showing a random 20 of 50 problems.
Example 1
hard
An octahedron has 8 equilateral triangular faces. If each side is 5, find its surface area using its net.
Example 2
medium
A triangular prism has equilateral triangular bases of side 6 and length 10. Find the total surface area from its net.
Example 3
hard
A pentagonal pyramid has a base that is a regular pentagon with side 4 and apothem ≈2.75, and triangular faces with slant height 6. Estimate the surface area from its net.
Example 4
hard
A right triangular prism has bases that are right triangles with legs 3 and 4, and prism length 10. Find its surface area using a net.
Example 5
medium
A cube has 11 distinct nets. How many of those nets are in the 'cross' or 'plus' shape (a center square with one square on each side and one extra at the bottom)?
Example 6
easy
Draw and describe the net of a rectangular prism (box) with dimensions 5 cm ×3 cm ×2 cm, and use the net to find the total surface area.Net of a rectangular prism (5 cm × 3 cm × 2 cm)
Example 7
hard
For a cone with base radius 3 and slant height 9, the lateral net is a sector. Find the central angle of that sector (in degrees).
Example 8
medium
A triangular prism has triangular bases of area 6 and three rectangular faces 4×10, 5×10, 3×10. Find the surface area from its net.
Example 9
easy
How many faces does the net of a cube have?
Example 10
challenge
A closed box 5×4×3 is to be gift-wrapped with paper exactly covering the surface plus 10% overlap. How much paper (area) is needed?Box with dimensions 5 × 4 × 3 to be gift-wrapped
Example 11
easy
Why are nets useful for finding surface area?
Example 12
easy
What 3D solid does a net consisting of 4 triangles fold into?
Example 13
hard
A cylindrical can has radius 3 cm and height 10 cm. Describe its net and find the total surface area.Cylinder with r
Example 14
medium
A rectangular box is 4×3×2. Using its net, find the surface area.Net of a rectangular box (4 × 3 × 2)
Example 15
medium
A cube net is shown with five of its squares totaling 80 cm². What is the total surface area of the cube?
Example 16
medium
A cylinder net has a rectangle of width 2π(5) and height 10, plus two circles of radius 5. Find the total area in terms of π.Cylinder with r = 5 and h = 10
Example 17
easy
What is a net of a 3D solid?
Example 18
medium
A cylinder has radius 2 and height 5. Find the total surface area in terms of π using its net.
Example 19
medium
Describe the net of a cone with base radius r and slant height ℓ.
Example 20
challenge
Explain why finding the shortest path for an ant crawling across a box's surface uses a net.