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Resources tagged with Volume and capacity similar to Volume of a Pyramid and a Cone:

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Volume of a Pyramid and a Cone

Stage: 3

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.

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The Genie in the Jar

Stage: 3 Challenge Level: Challenge Level:1

This jar used to hold perfumed oil. It contained enough oil to fill granid silver bottles. Each bottle held enough to fill ozvik golden goblets and each goblet held enough to fill vaswik crystal. . . .

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Cuboid Challenge

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

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Efficient Cutting

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

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Concrete Calculation

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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In a Spin

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

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Sliced

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

An irregular tetrahedron has two opposite sides the same length a and the line joining their midpoints is perpendicular to these two edges and is of length b. What is the volume of the tetrahedron?

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Boxed In

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Scientific Measurement

Stage: 4 Challenge Level: Challenge Level:1

Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.

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Mouhefanggai

Stage: 4

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.

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Thousands and Millions

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Here's a chance to work with large numbers...

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Sending a Parcel

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Zin Obelisk

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Qqq..cubed

Stage: 4 Challenge Level: Challenge Level:1

It is known that the area of the largest equilateral triangular section of a cube is 140sq cm. What is the side length of the cube? The distances between the centres of two adjacent faces of. . . .

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Funnel

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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 ?

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Plutarch's Boxes

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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2D-3D

Stage: 3 Challenge Level: Challenge Level:1

Two circles of equal size intersect and the centre of each circle is on the circumference of the other. What is the area of the intersection? Now imagine that the diagram represents two spheres of. . . .

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Conical Bottle

Stage: 4 Challenge Level: Challenge Level:1

A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone will the liquid rise?

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Immersion

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Various solids are lowered into a beaker of water. How does the water level rise in each case?

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Maths Filler 2

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you draw the height-time chart as this complicated vessel fills with water?

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Maths Filler

Stage: 4 Challenge Level: Challenge Level:1

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

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All in a Jumble

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

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Tubular Stand

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

If the radius of the tubing used to make this stand is r cm, what is the volume of tubing used?

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Cola Can

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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