1. Recap: Perimeter and Area
7. MEASUREMENT
Recap: Measurement Concepts
Prisms
Cylinders
Scale Factors
Spheres
Pyramids
Cones
Recap: Perimeter and Area
Building a 3-D Space

2. RECAP: MEASUREMENT CONCEPTS
Recap: Perimeter and Area
Building a 3-D Space

3. PRISMS Total Surface Area
TSA = (L x B) + (L x B) + (L x H) + (L x H) + (B x H) + (B x H)
= 2LB + 2LH + 2BH
Sum the areas of the panels of the rectangle to get the total surface area
Volume
= (L x B x H)

4. Example
Calculate the surface area and volume of the rectangular prism if it is closed on all sides. l = 8cm; b = 3cm ; h = 4cm
Surface Area = 2LB + 2LH + 2BH
Surface Area = 2(8) (3) + 2(8) (4) + 2(3) (4)
Surface Area =
Surface Area = 136 cm²
Calculate the surface area if the prism is open on top.
Surface Area = LB + 2LH + 2BH (TOP MISSING) Surface Area = (8) (3) + 2(8) (4) + 2(3) (4)
Surface Area = 112 cm²
Volume & Surface Area of a Right Prism
Challenge! Diagonal Length of a Rectangular Prism

5. Volume of Triangular Prisms
EXERCISE
Calculate the surface area and volume of a rectangular
prism in each of the following cases.
(a) the prism is closed and the dimensions are:
Length = 13 cm. Breadth = 6 cm and Height = 9 cm
(b) the prism is closed and the dimensions are:
Length = 12 m, Breadth = 5 m and Height = 7 m
(c) the prism is open on top and the dimensions are:
Length = 13 cm, Breadth = 6 cm and Height = 9 cm
(d) the prism is open on top and the dimensions are:
Length = 12 m, Breadth = 5 m and Height = 1 m
Volume of Triangular Prisms

6. CYLINDERS The Radius of a Circle Circumference of a Circle
Total Surface Area
A Cylinder & its Net
Proof: Curved Surface of a Cylinder = Rectangle

7. Volume Volume & Surface Area of a Cylinder Example
Calculate the Surface Area & Volume of Cylinders

8. Example Given a cylinder with r = 4cm and h = 6m:
(a) Calculate the surface area of the cylinder
assuming a closed cylinder
(b) Calculate the surface area of the cylinder
assuming an open-topped cylinder
(c) Calculate the volume of the cylinder

9. EXERCISE
Calculate the surface area and volume of a cylinder in each of the following cases:
(a) the cylinder is closed and the dimensions are:
radius = 5 cm and height = 3 cm.
(b) the cylinder is closed and the diameter = 12 cm
and the height = 7 cm.
(c) the cylinder is open and the dimensions are:
radius = 15 cm and height = 8 mm.
(d) the cylinder is open and the diameter = 4 cm
and the height = cm.

10. Enlarge the triangle by a scale factor of 3
SCALE FACTORS
It sometimes happens that the dimensions of the prism are changed.
For example, the length, breadth and height might be doubled.
The surface area and volume will then obviously be different from the original prism.
The number which is multiplied by each dimension is called a scale factor.
Enlarge the triangle by a scale factor of 3

11. Finding the New Enlarged Area
Example
If the length is x units and the breadth is y units, then the area of the rectangle is:
A = xy
If we now double the length and the breadth (multiply length and breadth by a scale factor of 2), then the area of the rectangle will change to:
A = (2x)(2y)
A = (2)(2)xy
A = 4xy
Therefore the new area is 4 times the original area.
Finding the New Enlarged Area

12. Fractional Scale Factor Enlargements
Note:
In general if the length and breath of a rectangle is multiplied by a scale factor of k units then the area of the rectangle will have been multiplied by k squared.
The new area is k squared times the original area.
Scale Factors and Area
Fractional Scale Factor Enlargements

13. Example Calculate the surface area and volume of the rectangular prism
if the length, breadth and height
are multiplied by a scale factor
of 5 units.
Surface Area = 2(5L)(5B) + 2(5L)(5H) + 2(5B)(5H)
Surface Area = 2(5 x 8)(5 x 3) + 2(5 x 8)(5 x 4) (5 x 3)(5 x 4)
Surface Area = 3400 cm²
Volume = (5L)(5B)(5H)
Volume = (5 x 8)(5 x 3)(5 x 4)
Volume = cm³
Therefore the new surface area is 5 x 5 times greater than the original surface area.

14. Identify the Scale Factor of Enlargement for each Circle
Note:
If the length, breadth and height are multiplied by a scale factor of k units, then:
Surface Area = 2(kL)(kB) + 2(kL)(kH) + 2(kB)(kH) Surface Area = k [2LB + 2LH + 2BH]
Volume = (k L) (k B) (k H)
Volume = k [LBH]
In general if the length, breadth and height of a
Rectangular prism are multiplied by a scale factor of k
units then the
surface area will be multiplied by k squared
volume will be multiplied by k cubed.
Identify the Scale Factor of Enlargement for each Circle

15. EXERCISE Consider the cylinder with the given dimensions:
r = 3cm ; h = 6cm.
(a) Calculate the surface area if the radius is doubled.
(b) Calculate the surface area if the radius is multiplied by 4cm.
(c) Calculate the surface area if the height is trebled.
(d) Calculate the volume if the radius is doubled.
(e) Calculate the volume if the radius is halved.

16. Challenge! Some Fun with Shapes: An Impossible Fork!
Area, Circumference & Volume Problems

17. Surface area = 4 Π r 2 Volume = SPHERES r is the radius
Volume of a Sphere Example
Calculate the Surface Area & Volume of Spheres

18. PYRAMIDS
Slant edges
Slant height
Perpendicular height

19. Calculate the SA & Volume of a Square Pyramid
Surface Area =area of base
+ ½ (perimeter of base) x slant height
Volume = 1/3 area of base
x perp height
Calculate the SA & Volume of a Square Pyramid

20. CONES TSA = area of base + area of curved surface = Π r 2 + Π r s
(s is slant height)
Volume = 1/3 ( area of base ) x ht
= 1 / 3 Π r2h
Calculate the Volume of the Cone
Recap: Identify the Shapes
Calculating the Height of a Cone