These are the topics related to the standard: Solve real-world and mathematical problems involving volume of cylinders, cones and spheres."
Here are some specific activities, investigations or visual aids picked out. Click anywhere in the grey area to access the resource.
Cylinders Apply formulae for the volumes and surface areas of cylinders to answer a wide variety of questions
Surface Area Work out the surface areas of common solid shapes in this collection of exercises.
Surface Area Video Finding the surface are of three dimensional shapes can involve some interesting formulae.
Volume Use formulae to solve problems involving the volumes of cuboids, cones, pyramids, prisms and composite solids.
Volume Video There are simple formulas that can be used to find the volumes of basic three-dimensional shapes.
Here are some exam-style questions on this statement:
- "The diagram shows a water tank in the shape of a cylinder. It has a diameter of 76cm anf a height of 36cm." ... more
- "Babatunde has to paint four containers." ... more
- "The volume of a cone can be calculated using the formula \(V=\frac13 \pi r^2 h \) and the area of the curved surface of a cone can be calculated using \(A= \pi r l\) (where \(r\) is the radius and \(l\) is the slant height)." ... more
- "A wedge is to be cut from a log in the shape of a cylinder as shown in the diagram below (not to scale)." ... more
Click on a topic below for suggested lesson starters, resources and activities from Transum.
- Circles This is all to do with pi and why it is such an important number. From finding the circumference and area of circles to problem solving and investigation. Pupils will begin by learning the names of the parts of a circle then, either through investigation or practical activity, discover that the circumference of a circle is always just a little more than three times the length of the diameter whatever the size of the circle. A brief walk through history leads them to find out how to use this knowledge (and a more accurate version of pi) to find the circumference and areas of circles. This can then be developed to find the area of a sector, area of a segment, area of an annulus and the area of the region between a circle and a square in more complex problem solving situations. More mathematics related to the circle can involve angle theorems, loci and algebra.
- Mensuration Mensuration is the branch of Mathematics dealing with measurement of angles, length, area, and volume. It is linked closely to the topic of Estimation and related to the topics of Angles, Shape and Shave (3D). It is essential for pupils to have an understanding of the units used to measure which include both the more common metric units and the Imperial units still in common usage. We have found a good teaching strategy is to ask each of the pupils to "Bring to the next Maths lesson some visual aid which will help the rest of the class remember the size of a unit of measurement". See Memorable Measures below for the printable resources. This activity provides an association with a unit, a visual aid and a known person which is a great memory enhancer.
- Shape (3D) A particular skill is required to be able to excel in this area of Mathematics. Spatial awareness is important for solving multi-step problems that arise in areas such as architecture, engineering, science, art, games, and everyday life. Children have varying abilities visualizing three dimensional relationships but these abilities can be developed through practical activities and working through mathematical problems. Breaking down three dimensional situations into smaller two dimensional parts in an important strategy for problem solving. See also the "Shape" Starters.
