Mathematics Surface Area

Lesson Objectives The aim of this powerpoint is to help you… to review the nets of common 3D shapes to apply the methods for finding the area of rectilinear shapes to finding the surface area of common 3D shapes

Cubes You should be able to recognise the net of a cube… remember a cube has 6 square faces The area of one face = length × width (in a square these are the same distance!) The total surface area of 6 faces = 6 × area of one square…

Example… Find the surface area of this cube… 2cm

Net & Surface Area One square face = 2 × 2 = 4cm² Total Surface area = 6 faces = 6 x 4 = 24cm² 2cm

Cuboids A cuboid can have all 3 dimensions different BUT there are still 6 faces. All the faces are rectangles and there are pairs that are the same (front & back / two sides / top and bottom) so you can work out the area of each rectangle and know it’s the same for another one!

Example… Find the surface area of this cuboid… 3cm 2cm 5cm TOP RT FRONT 2cm 5cm

Net & Surface Area TOP = 2 × 5 = 10cm² Bottom = same = 10cm² FRONT = 3 × 5 = 15cm² Back = same = 15cm² RIGHT = 3 × 2 = 6cm² Left = same = 6cm² Total surface area = 10+10+15+15+6+6 = 62cm² TOP 2cm FRONT RT 3cm 5cm

Did you notice…? Did you notice that for the cuboid we just had to multiply each of the 3 dimensions together in pairs? Let’s look at another example…

Example 2… Find the surface area of this cuboid… 5cm 3cm 8cm TOP RT FRONT 3cm 8cm

Solution without a net… Put the 3 dimensions (3, 5 and 8) into 3 different pairs and multiply… 3 × 5 = 15cm² (for Right & Left) 3 × 8 = 24cm² (for Top & Bottom) 5 × 8 = 40cm² (for Front & Back) Add 6 faces together = 15+15+24+24+40+40 = 158cm² 3cm 5cm 8cm FRONT TOP RT

Prisms & Cylinders Prisms have 2 end shapes. All the other faces are rectangles. For cylinders these end shapes are circles. There will be as many rectangles as there are edges to the end shape. For cylinders – just one rectangle whose length is the same distance as the circumference of the circle. Calculate the area of one end shape (and double for both ends) and add to this the area of each of the rectangles.

Example… Find the surface area of this L-shaped prism… 5cm 3cm 2cm 7cm FRONT TOP RT1 RT2 RT3 5cm 7cm

Net & Surface Area TOP = 3 × 7 = 21cm² LT = 7 × 7 = 49cm² BASE = 6 × 7 = 42cm² RT3 = 2 × 7 = 14cm² RT2 = 3 × 7 = 21cm² RT3 = 5 × 7 = 35cm² L-shapes are each 2 rectangles… FRONT = (3 × 5) + (6 × 2) = 27cm² BACK = (3 × 5) + (6 × 2) = 27cm² Total surface area = 21+49+42+14+21+35+27+27 = 236cm² FRONT TOP BACK LT BASE RT3 RT2 RT1 3cm 5cm 2cm 6cm 6cm 2cm 3cm 5cm 7cm

What next? Print out the notes called PAV4-SArea. Read through them and make sure you answer any questions. Work through the MyMaths lesson and its online homework called Nets, Surface Area found at: http://app.mymaths.co.uk/334-resource/nets-surface-area http://app.mymaths.co.uk/334-homework/nets-surface-area Save and complete the worksheet called SArea-S1.xlsx Now move on to the PAV5a powerpoint