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# Perimeter, Area and Volume - Stage 4

### Perimeter and Area

### Surface Area and Volume

### F'arc'tion

### Arclets

### Triangles and Petals

### Salinon

### Gutter

### Funnel

### Immersion

### Curvy Areas

### Track Design

### Fill Me up Too

### Perimeter, Area and Volume Short Problems

### Semicircle Distance

### Square in a Circle in a Square

### Sinking Feeling

### Half an Annulus

### Two Paths

### Bobbly Perimeter

### Cones and Spheres

### Ratio Cut

### Snake Eyes

### Loo Roll Emergency

### Candy Floss

### Similar Cylinders

### Ratio of Areas

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These resources are designed to encourage you to explore perimeter, area and volume of shapes and solids with curved edges and surfaces. For resources about perimeter, area and volume of shapes with straight edges, see our collection Perimeter, Area and Volume - Stage 3.

Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.

Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.

Age 14 to 16

Challenge Level

This selection of problems challenges you to use your understanding of perimeter and area of shapes made from circles.

Age 14 to 16

Challenge Level

This selection of problems challenges you to use your understanding of surface area and volume of three dimensional shapes based on circles.

Age 14 to 16

ShortChallenge 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 paper.

Age 14 to 16

Challenge Level

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

Age 14 to 16

Challenge Level

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

Age 14 to 16

Challenge Level

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

Age 14 to 16

Challenge Level

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

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

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

Age 14 to 16

Challenge Level

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

Age 14 to 16

Challenge Level

Where should runners start the 200m race so that they have all run the same distance by the finish?

Age 14 to 16

Challenge Level

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

Age 11 to 16

A collection of short problems on area and volume.

Age 14 to 16

ShortChallenge Level

Can you find the shortest distance between the semicircles given the area between them?

Age 14 to 16

ShortChallenge Level

What is the ratio of the areas of the squares in the diagram?

Age 14 to 16

ShortChallenge Level

Two vases are cylindrical in shape. Can you work out the original depth of the water in the larger vase?

Age 14 to 16

ShortChallenge Level

Can you locate the point on an annulus that splits it into two areas?

Age 14 to 16

ShortChallenge Level

Which of these two paths made of semicircles is shorter?

Age 14 to 16

ShortChallenge Level

Find the perimeter of this shape made of semicircles

Age 14 to 16

ShortChallenge Level

A solid metal cone is melted down and turned into spheres. How many spheres can be made?

Age 14 to 16

ShortChallenge Level

Cutting a rectangle from a corner to a point on the opposite side splits its area in the ratio 1:2. What is the ratio of a:b?

Age 14 to 16

ShortChallenge Level

Can you find the area of the yellow part of this snake's eye?

Age 14 to 16

ShortChallenge Level

When the roll of toilet paper is half as wide, what percentage of the paper is left?

Age 14 to 16

ShortChallenge Level

What length of candy floss can Rita spin from her cylinder of sugar?

Age 14 to 16

ShortChallenge Level

Two similar cylinders are formed from a block of metal. What is the volume of the smaller cylinder?

Age 14 to 16

ShortChallenge Level

What is the ratio of the area of the hexagon to the area of the triangle?