Volume and capacity

There are 55 NRICH Mathematical resources connected to Volume and capacity
Plutarch's Boxes
problem

Plutarch's boxes

Age
11 to 14
Challenge level
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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?
Zin Obelisk
problem

Zin obelisk

Age
11 to 14
Challenge level
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In the ancient city of Atlantis a solid rectangular object called a Zin was built in honour of the goddess Tina. Your task is to determine on which day of the week the obelisk was completed.
Concrete calculation
problem

Concrete calculation

Age
14 to 16
Challenge level
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The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to make the concrete raft for the foundations?
Volume of a Pyramid and a Cone
article

Volume of a pyramid and a cone

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
Mouhefanggai
article

Mouhefanggai

Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.