At the end of this lesson, you should be able to: 1. Calculate the volume and capacity of cubes and cuboids 2. Use 1cm 3 blocks to work out the volume of cubes and cuboid 3. Working out the depth, length, width of cubes and cuboids 4. Working out the surface area of cubes and cuboids 5. Working out the volume of prisms and cylinders 6. Working out the surface area of spheres, pyramids, cones and composite solids 7. identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres Worked Example 1 Work out the volume and surface area of the cuboid Surface Area = _________________ Volume = ______________________ Part 1 – Find the volume of the cuboid Volume = Length x width x height Volume = 7 x 4 x 3 Volume = 84 cm 3 Part 2 – Find the surface area of the cuboid Step 1 – Work out the area of the 3 faces Area of face 1 = 3 x 4 = 12cm 2 Area of face 2 = 3 x 7 = 21cm 2 Area of face 3 = 4 x 7 = 28cm 2 Step 2 – Add the areas of the 3 faces together 12cm 2 + 21cm 2 + 28cm 2 = 61 cm 2 Step 3 --- Multiply the answer from step 2 by 2 61 x 2 = 122 cm 2 Face 1 122 cm 2 84 cm 3 Topic 7: Volume
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
At the end of this lesson, you should be able to:
1. Calculate the volume and capacity of cubes and cuboids 2. Use 1cm3 blocks to work out the volume of cubes and cuboid
3. Working out the depth, length, width of cubes and cuboids
4. Working out the surface area of cubes and cuboids
5. Working out the volume of prisms and cylinders
6. Working out the surface area of spheres, pyramids, cones and composite solids
7. identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms,
cylinders, pyramids, cones and spheres
Worked Example 1
Work out the volume and surface area of the cuboid
Surface Area = _________________
Volume = ______________________
Part 1 – Find the volume of the cuboid
Volume = Length x width x height Volume = 7 x 4 x 3 Volume = 84 cm3
Part 2 – Find the surface area of the cuboid
Step 1 – Work out the area of the 3 faces
Area of face 1 = 3 x 4 = 12cm2 Area of face 2 = 3 x 7 = 21cm2 Area of face 3 = 4 x 7 = 28cm2
Step 2 – Add the areas of the 3 faces together
12cm2 + 21cm2 + 28cm2 = 61 cm2
Step 3 --- Multiply the answer from step 2 by 2
61 x 2 = 122 cm2
Face 1
122 cm2
84 cm3
Topic 7: Volume
Worked Example 2
Work out the volume of the triangular prism
Worked Example 3
Work out the volume the cylinder
Volume = ______________________
Volume = ______________________
Volume = Area of Cross Section x Length
Volume =( 4 x 3
2 ) x 7
Volume = 6 x 7
Volume = 42 Feet3
Volume = πr2h
Volume = π x (2)2 x 4
Volume = 16π or 50.24
42 Feet3
16π in3 or 50.24 in3
Topic 7: Volume
Worked Example 4
Work out the volume the sphere
Worked Example 5
Work out the volume the pyramid
Volume = ______________________
Volume = ______________________
Volume = 4
3 π 𝑟3
Volume = 4
3 x π x 63
Volume = = 4
3 x π x 216
Volume = 288π or 904.32
Volume = 1
3 x base area x height
Volume = 1
3 x ( 8 x 8) x 9
Volume = 1
3 x 9 x 64
Volume = 3 x 64
Volume = 192 cm3
288π m3 or 904.32 m3
192 cm3
Topic 7: Volume
Worked Example 6
Work out the volume of the cone
Worked Example 7
A sphere with a radius of 3cm is melted down and reformed into a solid cone. The cone is 4 cm high.
a. Calculate the radius of the base of the cone. Give your answer in exact form.
Volume = ______________________
Volume = ______________________
Volume = 1
3 π r2 h
Volume = 1
3 x π x 32 x 7
Volume = 1
3 x π x 9 x 7
Volume = 21 π m3
Step 1 – Find Volume of the sphere
V = 4
3 π r3
V = 4
3 x π x 33
V = 4
3 x π x 27
V = 36 π
Step 2 – Find the radius of the cone
V = 1
3 π r2h
36π = 1
3 x π r2 x 4
36 = 1
3 x r2 x 4
108 = 4r2
27 = r2
r = √27
21 π m3
√27 m
Topic 7: Volume
Surface Area formulas you need to know
Cone
Surface area of cone = πr2 + πrL
Topic 7: Volume
Practice Questions
Question 1
Answer = ___________________
Question 2
Answer = _________________
8m
8m
8m
9cm
3cm
12cm
Find the volume of the cuboid
Find the volume of the cube
Topic 7: Volume
Question 3
Answer = _______________
Question 4
Answer: _________________
18mm
18mm
10mm
1 8 m m
10m
Find the volume
of the cube
Find the volume of the cuboid
Topic 7: Volume
Question 5
Count the cubes and find the volume of each cube/cuboid. *Note* 1 Cube is equal to 1 cm3