### There are 17 results

Broad Topics >

Measuring and calculating with units > Surface and surface area

##### Age 11 to 14 Challenge Level:

How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

##### 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. . . .

##### 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:

Can you work out the dimensions of the three cubes?

##### 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?

##### 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?

##### Age 11 to 14 Challenge Level:

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

##### Age 7 to 16 Challenge Level:

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

##### 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?

##### 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 ?

##### Age 14 to 16 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?

##### 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 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?

##### Age 14 to 16 Challenge Level:

How much peel does an apple have?

##### 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?

##### 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. . . .