Resources tagged with: Surface and surface area

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There are 13 results

Broad Topics > Measuring and calculating with units > Surface and surface area

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?

When the Angles of a Triangle Don't Add up to 180 Degrees

Age 14 to 18

This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the. . . .


Age 14 to 16 Challenge Level:

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

Peeling the Apple or the Cone That Lost Its Head

Age 14 to 16 Challenge Level:

How much peel does an apple have?

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?

Painted Cube

Age 14 to 16 Challenge Level:

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

The Spider and the Fly

Age 14 to 16 Challenge Level:

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

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?

Tin Tight

Age 14 to 16 Challenge Level:

What's the most efficient proportion for a 1 litre tin of paint?

Three Cubes

Age 14 to 16 Challenge Level:

Can you work out the dimensions of the three cubes?

Cubic Conundrum

Age 7 to 16 Challenge Level:

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

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. . . .


Age 14 to 16 Short 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. . . .