Surface and surface area

problem

All Tied Up

Age

14 to 16

Challenge level

A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?
problem

Take Ten

Age

11 to 14

Challenge level

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?
problem

Cubic Conundrum

Age

7 to 16

Challenge level

Which of the following cubes can be made from these nets?
problem

Peeling the Apple or the Cone That Lost Its Head

Age

14 to 16

Challenge level

How much peel does an apple have?
problem

The Big Cheese

Age

7 to 11

Challenge level

Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?
problem

Tiles in the Garden

Age

7 to 11

Challenge level

How many tiles do we need to tile these patios?
problem

All Wrapped Up

Age

7 to 11

Challenge level

What is the largest cuboid you can wrap in an A3 sheet of paper?
problem

Tiling Into Slanted Rectangles

Age

7 to 11

Challenge level

A follow-up activity to Tiles in the Garden.
problem

Plutarch's Boxes

Age

11 to 14

Challenge level

According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes?
problem

F'arc'tion

Age

14 to 16

Challenge level

At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.