1. Carpentry & Joinery Phase 4 Volume, Mass & Density m³ kg Sample Questions & Solutions

2. Carpentry & Joinery Phase 4 Module 1 Unit 20 Volume Calculate the volume of the shapes below in m 3 Volume of cuboid = L x B x H Volume of large cuboid = 7.5 x 2.4 x 4.5 = 81m³ Volume of small cuboid = 5 x 2.4 x 1.8= 21.6m³ 59.4m³ Shape volume = 81 – 21.6 = 59.4m³ 38m 55m Volume = πr² x h = 3.14 x (38 x 38 )x 55 = 3.14 x 1,444 x 55 249,379 m 3 = 249,379 m 3 7.5m 2.4m 4.5m5m 1.8m

3. Carpentry & Joinery Phase 4Volume Find the volume of concrete required to fill twenty timber shutters measuring 2.5 meters in height and having a cross sectional area of 0.35m x 0.3m ? Answer = 20 (L x B x H) = 20 (0.35 x 0.3 x 2.5) 5.25m 3 of concrete = 5.25m 3 of concrete 2.5m 0.35m 0.3m

4. Carpentry & Joinery Phase 4Volume Calculate the volume of concrete required in order to pour a concrete raft foundation 9.3m x 2.7m, having a depth of 300mm and with a perimeter edge beam support of 300mm x 300mm Volume of main slab = L x B x H = 9.3 x 2.7 x 0.3 7.533m³ = 7.533m³ Volume of edge beam = 2(9.3 x 0.3 x 0.30 = 2(2.1* x 0.3 x 0.3) So total = 7.533 + 2(9.3 x 0.3 x 0.3) + 2(2.1 x 0.3 x 0.3 ) 9.585m³ of concrete = 9.585m³ of concrete *Note: edge beam measured full length on long sides so short sides are reduced by 2 x 0.3m to 2.1m Section through foundation 2.7m 300mm edge beam

5. Carpentry & Joinery Phase 4 Volume, Mass & Density Calculate the density of a load of hardwood with a total volume of 1.85m 3 and a mass of 975Kg. Density = Mass Volume Volume Answer; Density = 975 ÷ 1.85 = 527Kg/m 3

6. Carpentry & Joinery Phase 4 Volume, Mass & Density Calculate the volume of timber from the cutting list below. Calculate the total weight of the timber if the density of the timber is 430kg/m 3. Mass (Weight ) = Volume x Density)Mass (Weight ) = Volume x Density) Mass = 0.0756 x 430 32.508kg = 32.508kg No. OffLengthWidthThickness 17.2m100mm35mm 24.8m75mm35mm 21.8m75mm35mm 23m75mm35mm Total = 0.0756m 3 Volume (m 3 ) 0.0252 0.00945 0.01575 x x x x x x x x = = = = x x x x

7. Carpentry & Joinery Phase 4 Volume, Mass & Density Calculate the total mass (weight) of a load of 2 types of timber of the following density: (a) European Spruce 430kg/m 3 (b) Douglas Fir 527kg/m 3 If 20 planks 4.8m x 225mm x 75mm of each species are to be carried on a lorry Answer: Volume of each stack = 20(4.8 x 0.225 x 0.075) 1.62m 3 = 1.62m 3 696.6 kg Mass of European Spruce = 1.62 x 430 = 696.6 kg 853.74kg 1,550.34kg Mass of Douglas Fir = 1.62 x 527 = 853.74kg Total = 1,550.34kg