### There are 9 results

Broad Topics >

3D Geometry, Shape and Space > Cuboids

##### 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 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:

A box has faces with areas 3, 12 and 25 square centimetres. What is
the volume of the box?

##### 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:

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:

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

##### 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 11 to 14 Challenge Level:

What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?

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

Discover a way to sum square numbers by building cuboids from small
cubes. Can you picture how the sequence will grow?