1. Volumes Of Solids. 14cm 5 cm 7cm 4cm 6cm 10cm 3cm 4cm

2. What Is Volume ? The volume of a solid is the amount of space inside the solid. Consider the cylinder below: If we were to fill the cylinder with water the volume would be the amount of water the cylinder could hold:

3. Measuring Volume. Volume is measured in cubic units. Example: Written as 14 units 3 or 14 cu.units Here is a cubic centimeter It is a cube which measures 1cm in all directions. Length Width Height 1cm We will now see how to calculate the volume of various shapes.

4. Volumes Of Cuboids. Look at the cuboid below: 10cm 3cm 4cm We must first calculate the area of the base of the cuboid: The base is a rectangle measuring 10cm by 3cm: 3cm 10cm

5. 3cm 4cm 3cm 10cm Area of a rectangle = length x width Area = 10 x 3 Area = 30cm 2 We now know we can place 30 centimetre squares on the base of the cuboid. But we can also place 30 cubic centimetres on the base:

6. 10cm 3cm 4cm We have now got to find how many layers of 1cm cubes we can place in the cuboid: We can fit in 4 layers. Volume = 30 x 4 Volume = 120 cm 3 That means that we can place 120 of our cubes measuring a centimetre in all directions inside our cuboid.

7. 10cm 3cm 4cm Volume = 10 x 3 x 4 = 120 cm 3 This gives us our formula for the volume of a rectangular prism: Volume = ( length x width) x height V=Bh Base

8. What Goes In The Box ? Calculate the volume of the cuboids : (1) 14cm 5 cm 7cm 490cm 3 V = Bh V = ( 14 * 5) 7 V = (70) 7

9. What Goes In The Box ? Calculate the volume of the cuboids: (2) 3.4cm 39.3 cm 3 V = Bh V = (3.4 * 3.4) 3.4 V = (11.56) 3.4

10. What Goes In The Box ? Calculate the volumes of the cuboids below: (3) 8.9 m 2.7 m 3.2 m V = Bh V = (8.9 * 2.7) * 3.2 V = (24.03 ) 3.2 76.9 m 3

11. Volume of a Triangular Prism: What shape is it similar to? ___________ Rectangular Prism How does it compare to a rectangular prism? It is half a rectangular prism The base of the figure is made of_____________. Right triangle The formula for the area triangle is:___________ ½bh So, if the volume of a rectangular prism is ________ Bh What would we do to find half its volume: ____________ ½ the volume of rectangular prism

12. Find the volume of the prism. Using a Formula to Find the Volume of a Prism V = BhUse the formula. The base is a triangle. V = 6 · 6Substitute for B and h. V = 36 Multiply. The volume of the prism is 36 cm 3. · 3 · 4 = 1212 6

13. The Volume Of A Triangular Prism. Volume = Base x Height What shape is the base of the figure? Triangle. Calculate the area of the triangle: 5cm 8cm 5cm A = ½ x base x height A = 0.5 x 5 x 5 A = 12.5cm 2 The formula for the volume of a triangular prism is : V = ½ b h l B= base h = height l = length V = 12.5 (8) V = 100 cm 2

14. Find the volume of the prism. Example 2B 5 in 1.5 in. 4 in. V = Bh Use the formula. The base is a triangle. V = 3.75 · 4 B and h. V = 15 Multiply. The volume of the prism is 15 in 3. · 1.5 · 5 = 1212 3.75

15. The Volume Of A Cylinder. Consider the cylinder below: 4cm 6cm It has a height of 6cm. What is the size of the radius ? 2cm Volume = Base x height What shape is the base? Circle Calculate the area of the circle: A =  r 2 A = 3.14 x 2 x 2 A = 12.56 cm 2 Calculate the volume: V =  r 2 x h V = 12.56 x 6 V = 75.36 cm 3 The formula for the volume of a cylinder is: V =  r 2 h r = radius h = height.

16. What shape is the base?_____________ Circle Write the formula you would use to determine the area of the circle. ____________ A= πr 2 What other information do you need? ____________ Height of the cylinder d = 3.6 mm h = 7 mm V =πr 2 h To it altogether and what is your formula? ____________ The Volume Of A Cylinder.

17. What’s the formula?___________ V = πr 2 h V =π(5) 2 (8.3) V = π(25)(8.3) V = π(207.5) V =651.55 cm 3

18. What’s the formula?___________ V = πr 2 h V = π(2.4) 2 ( 9) V =π (5.76)(9) V = π(51.84) V =162.7777 V = 162.8 m 3

19. For storage Mrs. Lin uses cylindrical containers like the one shown below. If Mrs. Lin uses 2 of these containers, which is closest to the total volume of both containers? The Volume Of A Cylinder. F 50 cubic feet G 25.12 cubic feet H 50.24 cubic feet J 200.96 cubic feet 4 ft 2 ft

25. Summary Of Volume Formula. l b h V = l b h or Bh b l h V = ½ b h l or Bh