5 5 Volume and surface area Mathematical Studies
- Slides: 7
5. 5 Volume and surface area Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012
Volume and surface area The following presentation looks at how to calculate the volume and surface area of common three-dimensional shapes. Cube l l Volume = l × l = l 3 l To find the surface area, it is sometimes easier to visualise the shape as a net. l l Area of one square face = l × l = l 2 Area of six faces = 6 l 2 Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012
Volume and surface area Cuboid h Volume = l × w × h = lwh w l A possible net is shown below. lh wh lw lh l The area of each face is shown opposite. h h lw l w Total surface area = 2 wh + 2 lw + 2 lh = 2(wh + lw + lh) Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012
Volume and surface area Triangular prism x h l Volume = area of cross-section × length =½×b×h×l = ½bhl b Total surface area = sum of areas of each face To find the value of x use Pythagoras’ rule on the triangular face. Therefore Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 h x x b l
Volume and surface area Cylinder h r Volume = area of cross-section × height = π × r 2 × h = πr 2 h r Length of rectangle = circumference of circle = 2πr h Surface area = 2πr 2 + 2πrh = 2πr (r + h) Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012
Volume and surface area Cone l h Volume = r Surface area = area of base + area of curved face = πr 2 + πr l = πr (r + l) Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012
Volume and surface area Sphere r Volume = Surface area = 4πr 2 Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012
