Practice Nets in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

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 boxβ€”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 55, find its surface area using its net.

Example 2

medium
A triangular prism has equilateral triangular bases of side 66 and length 1010. Find the total surface area from its net.

Example 3

hard
A pentagonal pyramid has a base that is a regular pentagon with side 44 and apothem β‰ˆ2.75\approx 2.75, and triangular faces with slant height 66. Estimate the surface area from its net.

Example 4

hard
A right triangular prism has bases that are right triangles with legs 33 and 44, and prism length 1010. 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 55 cm Γ—3\times 3 cm Γ—2\times 2 cm, and use the net to find the total surface area.

Example 7

hard
For a cone with base radius 33 and slant height 99, 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 4Γ—104\times10, 5Γ—105\times10, 3Γ—103\times10. 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 5Γ—4Γ—3 is to be gift-wrapped with paper exactly covering the surface plus 10% overlap. How much paper (area) is needed?

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 33 cm and height 1010 cm. Describe its net and find the total surface area.

Example 14

medium
A rectangular box is 4Γ—3Γ—2. Using its net, find the surface area.

Example 15

medium
A cube net is shown with five of its squares totaling 8080 cmΒ². What is the total surface area of the cube?

Example 16

medium
A cylinder net has a rectangle of width 2Ο€(5)2\pi(5) and height 10, plus two circles of radius 5. Find the total area in terms of Ο€\pi.

Example 17

easy
What is a net of a 3D solid?

Example 18

medium
A cylinder has radius 22 and height 55. Find the total surface area in terms of Ο€\pi using its net.

Example 19

medium
Describe the net of a cone with base radius rr and slant height β„“\ell.

Example 20

challenge
Explain why finding the shortest path for an ant crawling across a box's surface uses a net.