Surface Area and Volume We use this equipment for the surface area and volume activity. Folding 2D/3D Geometric Solids - Set 12 (These can be purchased from www.hopeeducation.co.uk)

Starter Activity -Choose one of these 3D shapes and tell me everything that you can about it.

Learning Journey I can match a net to a 3D shape. Surface Area and Volume I can match a net to a 3D shape. I can identify edges, faces and vertices of 3D shapes. (Task A) I can find the surface area of a cube and cuboid by counting the squares on each face. I can find the volume of a cube and a cuboid by counting cubes. (Task B) I can find the surface area and volume of cuboids and triangular prisms (Task C) I can find the surface area and volume of prisms (Task D & Task E) I can calculate the volume of cones and pyramids. (Task F)

A B C Pupil hand-out. Print this slide and the next slide two to a page. D

E G F H Pupil hand-out, print this slide and the previous slide two to a page.

The face of this sculpture has been split into 3 large squares. Each of these squares is split into four smaller squares. Use the smaller squares on the face of this sculpture to calculate the perimeter and the area of the face. Each smaller square is 1m x 1m This Sculpture is a cuboid with a:- Length of 90cm Height of 88cm Width of 88cm. The circle has a diameter of 30cm

This sculpture is 93cm long across the top. This table has a semi-circular face and a rectangular top. The length across the rectangular top of the table is 160cm The width across the rectangular top of the table is 20cm. The height of the semi-circular face (without the legs) is 80cm This sculpture is 93cm long across the top. The perpendicular height of the sculpture is 76cm. The sculpture is 24cm deep. The sculpture is constructed from a solid piece of wood.

This fountain is a cylinder with a:- Diameter of 125cm Height of 300cm. This structure is a square based pyramid. The square has a side length of 5m The pyramid has a height of 8m.

These sculptures are cones. The radius of the circular face is 6m. The length of the cone (height) from the circular base to the tip is 8m. This sculpture is 3m high from the circular base to the top of the cylinder. The base has a radius of 90cm and a height of 60cm The cylinder has a radius of 50cm 3m 50cm 60cm 90cm

Match each 3D solid to its net. Task A Name each 3D Solid. Match each 3D solid to its net. Write down the number of edges, vertices and faces for each solid. Task B Draw the net of the cube and the cuboid on squared paper. Use the squares to calculate the surface area of the cube and the cuboid. Build a model of the cube and the cuboid using multi-link cube. Use this to calculate the volume of the solid. What is the same and what is different about the cube and the cuboid? Task C What is the minimum information that you need to know before you can work out the volume and the surface area of the cuboid and the triangular prism? Calculate the volume and surface area of the cuboid and the triangular prism. Task D Calculate the volume and the surface area of the cylinder. What is the minimum information that you would need to know before you could work out the volume and surface area of a cylinder? Task E Calculate the volume and the surface area of the pentagonal prism, the hexagonal prism, and the octagonal prism. Which 2D shapes did you use to help you work them out? What is the same and what is different about each prism? Task F Work out the volume of the pyramid and the cone. You can ask for a hint card to help you. How are the pyramid and the cone different from the prisms? How are the pyramid and the cone the same as the prisms? Main Activity – Pupils choose which task /tasks to work on.

Volume of a pyramid The volume of a pyramid is found by multiplying the area of its base A by its perpendicular height h and dividing by 3. Apex h slant height base A Hint Sheet - Stress that the height must be perpendicular from the base to the apex. Problems often give the slant height of a pyramid. The perpendicular height must then be found using Pythagoras’ Theorem. Volume of a pyramid = ⅓ × area of base × height V = ⅓ A h

Volume of a cone A cone is a special type of pyramid with a circular base. The volume of a pyramid can be found by multiplying the area of the base by the height and dividing by 3. The volume of a cone is given by: r h Volume = ⅓ × area of circular base × height Hint Sheet or V = ⅓ πr2h