ove. Stacked cubes do not make the footprint bigger; they only affect the height in an elevation. Five 1 cm cubes are arranged like this: - The front row has 3 cubes from left to right. - One cube is directly behind the left-hand cube. - One cube is stacked on top of the right-hand front cube. Draw the plan and the right side elevation. 1. For the plan, look from above. Mark every floor position that has at least one cube on it. 2. The plan has 3 squares in the front row, plus 1 square behind the left-hand square. 3. For the right side elevation, look from the right. The front depth position has maximum height 2 cubes because of the stack. 4. The back depth position has maximum height 1 cube. 5. Draw the side elevation as two depth columns: the front column 2 squares high, and the back column 1 square high. If a tower is 3 cubes high, its plan still shows only one square, because from above you only see its footprint. ## Curved and pointed solids For circles, the **radius** is the distance from the centre to the edge. The **diameter** is the full distance across the circle through the centre, so it is twice the radius. For cones and pyramids, the **apex** is the pointed top. The **perpendicular height** is the straight vertical height from the base to the apex, at 90° to the base. - A cylinder has a circular plan and rectangular elevations. - A cone has a circular plan and triangular elevations. - A square-based pyramid has a square plan and triangular elevations. A cone has radius 2 cm and perpendicular height 5 cm. Draw its plan and side elevation. 1. The plan is the view from above, so you see the circular base. 2. The radius is 2 cm, so the diameter is 4 cm. Draw a circle 4 cm across. 3. The side elevation of a cone is an isosceles triangle. 4. The base of the triangle is the diameter, 4 cm, and the vertical height is 5 cm. 5. Put the apex above the midpoint of the base, then join the apex to both ends of the base. For a cone or pyramid, the height of the elevation is normally the **perpendicular height**, not the sloping edge, unless the question specifically tells you otherwise. ## Using a scale A **scale** tells you how a length on the drawing matches a real length. For example, a scale of 2 cm to 1 m means every real metre is drawn as 2 cm on the grid. Always convert the real measurements before drawing. A square-based pyramid has base side 250 cm and perpendicular height 350 cm. Draw the plan and front elevation using a scale of 2 cm to 1 m. 1. The scale uses metres, so first convert the real measurements into metres. Remember that 100 cm is 1 m. 2. Apply the scale 2 cm to 1 m: $$ \begin{aligned} 250\text{ cm} &= 2.5\text{ m} \to 5\text{ cm on the drawing} \\ 350\text{ cm} &= 3.5\text{ m} \to 7\text{ cm on the drawing} \end{aligned} $$ 3. The plan of a square-based pyramid is a square, so draw a 5 cm by 5 cm square. 4. To show the pyramid shape in the plan, mark the centre of the square and join it to the corners. 5. The front elevation is a triangle with base 5 cm and vertical height 7 cm. 6. Put the apex directly above the midpoint of the base, then join it to both ends of the base. If the scale is 2 cm to 1 m, a real length of 3 m is drawn as 6 cm, not 3 cm. 1. First identify the viewing directions: plan, front elevation and side elevation. 2. Match dimensions carefully: width with width, depth with depth, height with height. 3. If a scale is given, convert every length before you start drawing. 4. Use the grid squares neatly and label important dimensions on your sketch.