4cm 5cm 9cm² 5cm 4.5cm 2.5cm

What’s the same and what’s different?? Discuss… What’s the same and what’s different??

The volume of a solid is the amount of space occupied by the solid. The greater the volume of a solid the more space it takes up. The volume of a solid is the number of unit cubes that the solid can be divided into. 2 units 1 unit 1 unit 1 unit 4 units 24 unit cubes altogether 3 units

This cuboid is made up of centimetre cubes (cm³). What is its volume?

What is the volume of this cuboid? 5 cm 2 cm 10 cm 100 cm³

What is the volume of this cuboid?

Answers 5 x 2 x 7 = 70 cm3 3 x 2 x 8 = 48 cm3 5 x 6 x 2 = 60 cm3 2 x 2 x 6 = 24 cm3 5 x 2 x 3 = 30 cm3 2 x 7 x 4 = 56 cm3 7 x 7 x 2 = 98 cm3 2 x 4 x 5 = 40 cm3 2 x 9 x 2 = 36 cm3 Extension question: 54 ÷ (9 x 2) = 54 ÷ 18 = 3cm

Josh is having a birthday party Josh is having a birthday party! He wants to make boxes of sweets to give to his guests. He starts with a square piece of paper that measures 20cm x 20cm. How big should the squares be that he cuts out of the corners to maximise the volume of the box?

Record your results in the table provided. Don’t forget your units of measurements!

Extension questions What if the square you cut out doesn’t have to use whole number measurements (e.g. 2.4cm)? Would this change your answer? What if you started from a 10cm x 20cm rectangle instead? What would the biggest volume be?

Surface areas of cubes and cuboids What is surface area? width Think about finding the area of a square or rectangle… height Area = height x width What about if we phrase surface area differently… The area of the surface

Surface areas of cubes and cuboids The area of the surface How could we find the surface area of a cuboid using the height, width and length? W L How many faces does a cuboid have? H 6 So we could add together the areas of all 6 faces!

Surface area = Front Back Left Right Top Bottom (Length x Height) + W Back Top Left Surface area = Front Right Front Back Left Right Top Bottom (Length x Height) + (Height x Width) + (Length x Width) + (Length x Width) Bottom By adding the area of all of the faces, we can find the surface area of the whole cuboid.

Answers 38cm² 168cm² 62cm² 68cm²

A cube is cut out of a larger cube and stuck into the corner, as shown A cube is cut out of a larger cube and stuck into the corner, as shown. What is the surface area of the resulting shape? All lengths are in centimetres

HINT: There are 15 faces!

Total Surface Area = 115cm²

Calculate the areas of the following shapes Starter Calculate the areas of the following shapes 3cm 4cm 5cm 4cm 3cm 5cm 6cm

Calculate the areas of the following shapes Starter Calculate the areas of the following shapes 3cm 15cm² 4cm 16cm² 5cm 4cm 3cm 5cm 15cm² 28.26cm² 6cm

Cross Section – The shape of the slice Prism – A shape that has the same cross section all the way through

A prism is a 3-D shape which has the same cross-section throughout its height. Triangular prism Pentagonal prism Cuboid

Identify the prisms

= area of cross-section x vertical height Volume of a prism = area of cross-section x vertical height Cross-section Vertical height

= area of cross-section x vertical height Volume of a prism = area of cross-section x vertical height Example: Find the volume of this prism 25 x 7 = 175 cm³ 25 cm2 7 cm

= area of cross-section x vertical height Volume of a prism = area of cross-section x vertical height Example: Find the volume of this prism Area of cross-section = ½ x 6 x 3 = 9 cm² 3 cm 10 cm Volume = 9 x 10 = 90 cm³ 6 cm

Checkpoint 100mm³ 72cm³ 2 90cm³ 120m³ 5cm 5m 6m 250cm³

Volume of Prisms Thoughts and crosses Calculate the volumes of 4 of the prisms, either vertically, horizontally or diagonally

The area of the surface How could we find the surface area of a triangular prism using the height, width, depth and slant height? S H D How many faces does a triangular prism have? W 5 So we could add together the areas of all 5 faces!

S Surface area = H Front Back Left Right Bottom (Width x Height ÷ 2) + (Height x Depth) + (Slant x Depth) + (Width x Depth) D W Bottom By adding the area of all of the faces, we can find the surface area of the whole triangular prism.

Answers 36cm² 240cm² 352cm² 372cm²

Calculate the areas and circumferences of these circles to 1 d.p. Starter Calculate the areas and circumferences of these circles to 1 d.p. Q1 Q2 Q3 2.5 cm 7 cm 8 cm Q4 Q5 Q6 3 cm 4.5 cm 2 cm

Answers Q1 A = 38.5 cm², C = 22.0 cm Q2 A = 19.6 cm², C = 15.7 cm

Volume of a prism = area of cross section x length Calculate the volume of this cylinder. Give your answer to 1 d.p. Area of cross-section = π x 12² = 452.389… cm² Volume = 452.389… x 20 = 9047.8 cm³ Calculate the volume of this cylinder. Give your answer to 3 s.f. Area of cross-section = π x 5² = 78.539… cm² Volume = 78.539… x 12 = 943 cm³

Answers 150.80cm³ 18.85cm³ 192.42cm³ 1194.59cm³ 150.80cm³ 192.42cm³ 1194.59cm³ 18.85cm³ 2.27cm 2.90cm 5.27cm 5.57cm

πd h Circumference = πd Height (h) Surface area of curved part of cylinder = πdh

Surface area of cylinder = 2πr² + πdh Area of top circle = πr² Surface area of curved part of cylinder = πdh Area of bottom circle = πr² Surface area of cylinder = 2πr² + πdh

Calculate the total surface area of the cylinder, giving your answer to 1 d.p.: Top = π x 2² = 12.566… cm² 4cm Curved = π x 4 x 6 = 75.398… cm² Bottom = π x 2² = 12.566… cm² Total = 12.566… + 75.398… + 12.566… 6cm = 100.5 cm²

192 cm² 10995.6 cm²

Answers 175.93cm² 186.92cm² 43.98cm² 633.03cm² 175.93cm² 186.92cm² 43.98cm² 633.03cm² 19.06cm 28.92cm 111.75cm 63.90cm

Starter Calculate the volume of the cuboid and the area of the circle. Give your answers to 3 s.f. where appropriate. 94 cm 9 m 89 cm 140 cm 1 170 000 cm³ or 1.17 m³ 63.6 m²

Volume of Pyramids Volume of pyramid = 1 3 x base area x vertical height Calculate the volume of the pyramids below: 1 3 x 20 x 13 x 12 = 1040 cm³ 1 3 x 7 x 4 x 6 = 56 cm³

Volume of Pyramids Volume of pyramid = 1 3 x base area x vertical height A cone is a circular-based pyramid! Calculate the volume and give your answers to 1 d.p. 6 mm 8 cm 11 mm 5 cm 1 3 x π x 5.5² x 6 = 190.1 mm³ 1 3 x π x 5² x 8 = 209.4 cm³

Answers 70 cm3 314.16 cm3 12 cm3 m = 12.5 cm n = 1.31 cm

Answers 70 cm3 314.16 cm3 12 cm3 m = 12.5 cm n = 1.31 cm

? cm 3 cm 4 cm 6 5 7 4

? cm 3 cm 4 cm 6 5 7 4

9 cm 6 cm ? cm 6.7 12 10.8 13.6

9 cm 6 cm ? cm 6.7 12 10.8 13.6

8 cm ? cm 3 cm 7.4 8.5 9.3 6.6

8 cm ? cm 3 cm 7.4 8.5 9.3 6.6

Surface Area of Cones Surface area of cone = πr² + πrl l h r Curved surface area (you get given this bit in exams!) Area of base r Calculate the surface area of this cone. Give your answer to 1 d.p. (π x 4²) + (π x 4 x 9) = 163.4 cm² 9 cm 4 cm

Surface Area of Cones Surface area of cone = πr² + πrl l h r Curved surface area (you get given this bit in exams!) Area of base r Sometimes, we need to calculate l first. l = 6 2 + 4 2 = 7.211… cm 6 cm (π x 4²) + (π x 4 x 7.211…) = 140.9 cm² 4 cm

Volume of a sphere = 4/3 x π x r³ Surface area of a sphere = 4 x π x r² Calculate the volume and surface area of the sphere below: Volume = 4/3 x π x 8³ = 2144.7 cm³ 8cm Surface area = 4 x π x 8² = 804.2 cm² 54

Answers 1) a) V = 113.1cm³, SA = 113.1cm² b) V = 904.8cm³, SA = 452.4cm² c) V = 4188.8cm³, SA = 1256.6cm² d) V = 1436.8cm³, SA = 615.8cm² e) V = 179.6cm³, SA = 153.9cm² f) V = 47.7cm³, SA = 63.6cm² 2) a) 1963.5cm² b) 8181.2cm³ 3) V = 14137.2cm³, height = 125cm