Surface Area. Prisms and Cylinders
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1 Surface Area Prisms and Cylinders Following are a series of questions on calculating the surface area of Prisms and Cylinders. You do not have to answer all questions. When you feel comfortable with a particular colour of question move on to the next colour ( Green Blue Red). Towards the end of the lesson you will be asked to indicate on the Dartboard below the colour of question(s) completed. 1. Progress check Dartboard Work in your pair/groups and enjoy. If there are any (task related) questions please feel free to ask each other ;- )
2 Prism 1 - ( Triangle based prism) Below is a piece of a toy that needs to be painted. You have been asked to calculate its surface area. 10cm 9cm 20cm 9cm Face number/name Dimensions of the face Area of the face Total surface area GREEN
3 Prism 2 - ( Compound shape based prism) Below is a piece of a toy that needs to be painted. You have been asked to calculate its surface area. 30cm 10cm 9cm 15cm 4cm GREEN
4 Prism 3 - ( Trapezium based prism) You work for a company that produces props for Hollywood. Below is a fake gold bar that needs painting. In order to calculate the final cost of each gold bar the paint department needs to know the surface area of the bar. Calculate the surface area of the gold bar. 3cm 4cm 3cm 20cm 5cm BLUE
5 Cylinder- 4 You have just finished designing a prototype filter for the next Dyson Air Purification System (DAPS). In order to test its efficiency you need to calculate the surface area of the filter. Calculate the surface area of the prototype filter. 4.5cm 9cm BLUE
6 Prism 5 - ( Cube cut- out) Below are two revolutionary prototype designs for Solar Energy production both having the same exterior dimensions. Design 1.. 3mm 1mm 2 produces 0.5mWh 5mm 3mm 5mm 5mm Design 2. Is a cube with 5mm sides it produces 0.6mWh per 1mm 2 of area. Which one is more efficient at producing electricity? And why do you think this is? RED
7 Cylinder- 6 - (Cylinder cut- out) Below is a component for the MagLev train system (trains using magnetic levitation to reach speeds of over 300 mph). The component needs to be electroplated (process of coating) with Beryllium (Be) an extremely expensive superconductor. 30mm 20cm 10mm 1) Calculate the surface area of the component. 2) If 1g of Beryllium coats 0.1m 2 calculate the amount of Beryllium needed to coat the component once. Hint: think about how many cm 2 are equivalent to 1m 2 RED
8 Worded problems. 1) A room has dimensions 6.8 metres x 9.2 metres x 2.5 metres. Stephanie wants to paint the walls of the room. A large tin of paint covers 20 m 2 and costs Ignoring windows and doors, and allowing for two coats of paint, how much will it cost Stephanie to paint the room? 2) A cube has a surface area of 24 cm 2. Work out the length of the side of the cube. GREEN
9 Hints sheet Are you really! sure you need this if so keep on reading. Prism- 1 Step 1 work out how many faces the prism has remember to include the ends. List the dimensions of each face. Remember to calculate the area of a triangle you multiply the base by the height (perpendicular) and divide your answer by 2 ( ½ b x h ) Now add together the area of each face and remember the correct units. Prism- 2 This time the end shape is a compound shape so you will have to split it up into two rectangles. Now you can label the dimensions of the two rectangles List the dimensions of the other faces. Prism- 3 Same steps as Prism- 1 but this time remember the ends are trapeziums refer to the Recap sheet on how to calculate the area of a trapezium.
10 Cylinder- 4 You will need to calculate the area of the end faces of the cylinder (circles), refer to Recap sheet. Now you will need to calculate the area of the curved surface. Look at the net of a cylinder below how would you calculate the dimension of the missing side? 4.5cm? work this out 9 cm Prism- 5 Use the tablets to identify all the faces. Cylinder- 6 Similar method as Cylinder- 4 but remember there is also a cylinder inside the larger one. Pay attention to the units.
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