Surface and surface area

There are 25 NRICH Mathematical resources connected to Surface and surface area

problem

Tiles in the garden

Age

7 to 11

Challenge level

How many tiles do we need to tile these patios?

problem

Wrapping presents

Age

7 to 11

Challenge level

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

problem

Four points on a cube

Age

16 to 18

Challenge level

What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O?

problem

Uniform units

Age

14 to 16

Challenge level

Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?

problem

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.

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

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

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

Inside out

Age

14 to 16

Challenge level

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you can colour every face of all of the smaller cubes?

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For younger learners

Surface and surface area

Tiles in the garden

Wrapping presents

Four points on a cube

Uniform units

F'arc'tion

Plutarch's boxes

Take ten

Cubic conundrum

All tied up

Inside out