# Surface Area and Volume

Students are required to know what is meant by the surface area of a solid, be able to calculate the surface area of a variety of solids and to be able to solve problems relating to surface area. Students are also expected to understand what is meant by the volume of a solid, be able to find the volumes of a variety of solids and to be able to solve problems relating to volume. This resource package contains a number of activities which require students to solve problems involving cross-sectional areas, surface area and volume of cubes, cuboids, prisms, cylinders and composite solids.

Visit the secondary mathematics webpage to access all lists.

### Surface Area and Volume

This resource contains two packs of games, investigations, worksheets and practical activities.

In pack one appropriate activities are **How Many Cubes?, Layers, Block problems **and **Volumes**, all of which use blocks to visualise and find the volume of cubes, cuboids and prisms.

In pack two, **Volume of Cuboids, Volume of Prism and Volumes** and **Surface Areas of Cylinders** all use formulae to find volumes.

### Area, Perimeter and Volume

The text book ‘**Area, Perimeter and Volume’ **includes a review of the names and shapes of common two dimensional shapes; areas of special shapes such as circle, triangle, parallelogram and composite shapes; the perimeter of special shapes such as the circumference of a circle, the perimeter of composite shapes, finding a formula for perimeter using algebra; surface area and volume of three dimensional shapes including the cube, cuboid, cylinder and prism.

In the activities file, ‘**Surface area of a Cylinder’ **is a practical activity in which students investigate connections between the area of a rectangle, the radius of the cylinder this rectangle makes when rolled into that shape and the height of the cylinder formed.

**‘Density of Flood’ **uses volume and mass of different tins to calculate the density of the contents of the tin.

### Keeping Baby Warm

In this activity students compare the ratio of surface area to volume in adults and babies and are asked to explain how babies are kept wrapped up in winter.

In order to carry out the task, students are required to calculate surface area and volume and make scale models of a baby and an adult. The models may be simple in nature, such as a single cuboid, or a more complex model involving a variety of cuboids, cylinders or even spheres.

### Boxes and Bottles

These activities explore some of the mathematics behind packaging decisions taken by manufacturers, they provide a platform for students to make conjectures and find efficient ways of recording results to justify claims they have made.

In ‘**Boxing Stock Cubes’ **students use 36 multilink cubes to explore the number of different cuboids that can be made with a constant volume.

Exploring nets is the focus of ‘**Folding Cubes’**. Here students are challenged to find as many different arrangements of 6 squares as they can. When the pupils have found the 11 nets of a cube they then have to decide which would be the best to use to create boxes to hold eight 1cm cubes of sugar.

In ‘**How Much Does it Hold?’**, students order and estimate the capacity of a range of containers, before trying to half fill each of them and check their accuracy with a measuring jug.

### Packaging

This rich activity explores flat designs which can be folded and used to package food and drink and provides experience of visualising three dimensional shapes from two dimensional representations.

In **Four Chocolates** and **It Takes the Biscuit**!, students measure accurately and construct accurate diagrams in order to make a box in which to package biscuits and a carrier bag in which to hold the box. **Four Chocolates** draws on and develops understanding of relationships between linear dimensions and volume.

### Boxes

This resource develops an understanding of volume and surface area of three dimensional objects through exploring nets.

The unit looks at perimeter, area and volume in context. In addition, there are opportunities to develop visualisation and problem-solving skills, to use ICT and there are opportunities for practical work in all of the lessons.

Students are required to perform a number of related tasks including know and use the formula for the volume of a cuboid; calculate volumes and surface areas of cuboids and shapes made from cuboids. (Measures: step 7) and calculate the surface areas and volumes of right prisms; calculate lengths, areas and volumes in right prisms, including cylinders. (Measures: step 9)

### Mensuration

This resource is a mixed selection of worksheets requiring students to answer questions about the dimensions of the square, the circle, sectors of circles, the cube, the cylinder and the sphere. The resource begins with teacher notes to provide some additional background information. These notes are intended only to provide some additional background alongside some suggestions to guide teaching and learning. This resource would probably be best used for revision or to challenge learners existing knowledge. Many of the examples are of a practical nature. The others require the ability to manipulate the appropriate formulas. It includes:

Cubes and spheres: Students are required to find the volume, the total surface area and a range of other dimensions relating to cubes, spheres and hemispheres.

Practical cylinders: Contains questions requiring students to find the height, diameter, curved surface area and volume of cylinders. There are also some packing problems.

### Cuboid faces

In this teacher presentation and collection of student worksheets, the area of each face of a cuboid is given. Students are then asked to calculate the volume.

Each student worksheet contains a different cuboid, but the solutions all have something in common. The teacher presentations highlights two possible ways of finding the general solution