Find the length of the diagonal AC Hence, or otherwise, find the length of the space diagonal AG

1. Level 1 -> 1) Find the length of the diagonal AC Hence, or otherwise, find the length of the space diagonal AG 2) Find exactly half the length of the diagonal AC Hence, or otherwise, find the perpendicular height of this pyramid (where E is directly above the centre of the base) I can recall and use Pythagoras‘ Theorem

2. Level 2 1) Without bending, what is the length of the longest straw that will fit entirely inside this cylindrical can? 15cm 2) 8cm The Great Pyramid of Cheops is 140m high, and the sides of its square base are of length 229m. (where the apex is directly above the centre of the base) What is the slant height (as shown)? I can comprehend and solve 3D problems using Pythagoras’ Theorem }

3. Level 3 1) A spider is sitting exactly in the middle of one of the smallest walls in a living room, whilst a fly is resting by the side of the window on the opposite wall, 1.5m above the ground and 0.5m from the adjacent wall. • Work out the distance between spider and fly • As the spider wishes to conserve his silk, he would rather crawl along the walls. Assuming he takes the shortest route, how far would he travel? 2) • Consider a cube with sides 4cm, what is the angle of • elevation from one of the bottom corners to its diagonally • opposite top corner? Extension: Following on from (2b), if the fly were further down the wall, at what point would the spider be better off using the side walls? } I can analyse and investigate 3D problems, knowing when to apply Pythagoras’ Theorem

4. Level 1 1) Find the length of the diagonal AC Hence, or otherwise, find the length of the space diagonal AG 2) Find exactly half the length of the diagonal AC Hence, or otherwise, find the perpendicular height of this pyramid (where E is directly above the centre of the base) Answers to 2.d.p: a) 30.46cm b) 34.41cm a) 7.43cm b) 16.39cm

5. Level 2 1) Without bending, what is the length of the longest straw that will fit entirely inside this cylindrical can? 15cm 2) 8cm The Great Pyramid of Cheops is 140m high, and the sides of its square base are of length 229m. (where the apex is directly above the centre of the base) What is the slant height (as shown)? Answers to 2.d.p: 17cm 214.06m

6. Level 3 1) A spider is sitting exactly in the middle of one of the smallest walls in a living room, whilst a fly is resting by the side of the window on the opposite wall, 1.5m above the ground and 0.5m from the adjacent wall. • Work out the distance between spider and fly • As the spider wishes to conserve his silk, he would rather crawl along the walls. Assuming he takes the shortest route, how far would he travel? 2) • Consider a cube with sides 4cm, what is the angle of • elevation from one of the bottom corners to its diagonally • opposite top corner? Extension: Following on from (2b), if the fly were further down the wall, at what point would the spider be better off using the side walls? Answers to 2.d.p: a) 5.23m b) 7.40m 2) 35.26°