which measure would a tile installer care the most about: perimeter, area, or volume? how are these...
TRANSCRIPT
Which measure would a tile installer care the most about: perimeter, area, or volume?
How are these measures different?
Perimeter, Area, and Volume
1
CAnswer
1 Perimeter, Area, and Volume
1 Which statement describes the correct relationship between the sides of this right triangle?
A a2 + c2 = b2
B b2 + c2 = a2
C a2 + b2 = c2
D b2 – a2 = c2
cb
a
Getting Ready
B
Getting Ready
8 cm
6 cm
5 cm
3 cm
9 cm
10 cm
5 cm
5 cm
2 Which shape has the greater perimeter?
A B
Answer
1 Perimeter, Area, and Volume
B
3 Which shape has the greater area?
A B
Getting Ready
6 cm
5 cm
3 cm
9 cm
4 cm
5 cm
5 cm
10 cm
Answer
1 Perimeter, Area, and Volume
A
4 Which simple shapes make up thiscomposite shape?
A three triangles and a rectangle
B two triangles and a square
C a triangle, a rectangle, and a square
D a triangle, a rhombus, and a square
Answer
Getting Ready
1 Perimeter, Area, and Volume
D
A Formula for the area of a rectangle: A = l × w, where l represents the length andw represents the width
B
C
D
Formula for the area of a triangle:
A = , where b represents the base and
h represents the height
Formula for the area of a parallelogram: A = b × h, where b represents the base andh represents the heightFormula for the area of a circle: A = 2πr, where r represents the radius ofthe circle
5 Which formula is not correct?
2b × h
Answer
Getting Ready
1 Perimeter, Area, and Volume
B
6 Which expression would you use to calculate the volume of this rectangular prism?
A 2(3 cm)(3 cm) + 4(3 cm)(6 cm)
B (3 cm)(6 cm)(3 cm)
C (3 cm + 6 cm + 3 cm + 6 cm)(3 cm)
D 2(3 cm + 6 cm + 3 cm)
3 cm
3 cm
6 cm
6 cm3
cm
3 cm
Answer
Getting Ready
1 Perimeter, Area, and Volume
D
7 Which expression would you use to calculate the volume of this cylinder?
A 2π(8 cm) + 2π(4 cm)(9 cm)
B 2π(4 cm)(9 cm)
C π(9 cm)2(4 cm)
D π(4 cm)2(9 cm)
4 cm
9 cm
Answer
Getting Ready
1 Perimeter, Area, and Volume
...is equal to the area of the square on the hypotenuse.
The sum of the area of the squares on the legs of a right triangle...
cb
b
a
a
c
c2
b2
a2
Mid-Chapter FAQ
How does the geometric representation of the Pythagorean theorem relate to the algebraic representation a2 + b2 = c2?
Q
A
1 Perimeter, Area, and Volume
Reveal
Why is the Pythagorean theorem useful?Q
If you know the lengths of two of the sides of a right triangle, you can determine the lengthof the third side.
A1
A2
If you know the areas of two of the squares on the sides of a right triangle, you can determine the area of the third square and the lengths of all the sides.
6 cm
5 cm
36 cm
25 cm
Mid-Chapter FAQ
1 Perimeter, Area, and Volume
Reveal
How do you determine the perimeter of a composite shape?
The perimeter of a composite shape is the total distance around the shape.
Sides that lie inside the composite shape are not counted in the perimeter.
When a composite shape includes a circle or a part of a circle, use the formula for the circumference of a circle,
C = πd or C = 2πr,
where C represents the circumference, d represents the diameter, and r represents the radius.
Q
A
Mid-Chapter FAQ
1 Perimeter, Area, and Volume
Reveal
How do you estimate the area of a shape?Q
Impose a grid of known size and count the squares.
A1
A2 Create a simple shape that has an area close to the area of the shape. Use the known measurements of the simple shape to estimate the area of the shape.
A3 Decompose the shape into simple shapes, or cover the shape with several simple shapes. Use known measurements of the simple shapesto estimate the area of the shape.
Tech
Tip
Mid-Chapter FAQ
1 Perimeter, Area, and Volume
Reveal
How do you determine the area of a composite shape?
Follow these steps:
1. Decompose the shape into simple shapes. (There may be many ways to decompose the shape, but will all result in the same calculated area.)
2. Calculate the areas of the simple shapes using the operations and formulas you already know.
3. Add the areas of the simple shapes. (You may have to subtract areas for holes.)
Q
A
10 cm
10 cm
Mid-Chapter FAQ
1 Perimeter, Area, and Volume
Reveal
volume of prism
Chapter FAQ
How is the volume of a prism related to the volume of a pyramid?
Q
A When a prism and a pyramid have the same base shape, with the same dimensions and the same vertical height, h, they have the following relationship:
volume of pyramid =
volume of pyramid =
3
3(area of base)h
area of base
h
area of base
h
1 Perimeter, Area, and Volume
Reveal
How is the volume of a cylinder related to the volume of a cone?
Q
A When a cylinder and a cone have the same radius, r, and the same vertical height, h, they have the following relationship:
volume of cone =
volume of cone =
volume of cone =
volume of cylinder
3
(area of base)h3
πr 2h3
hr
hr
Chapter FAQ
1 Perimeter, Area, and Volume
Reveal
How is the volume of a sphere related to the volume of a cone?
Q
A When a sphere and a cone have the same radius, r, and the height, h, of the cone equals the diameter, d, of the sphere, they have the following relationship:
volume of sphere = 2(volume of cone)
volume of sphere =
volume of sphere =
volume of sphere =
2(πr 2h)
32(πr
2)(2r)3
4πr 3
3
hr
rd
Chapter FAQ
1 Perimeter, Area, and Volume
Reveal
How is the volume of a sphere related to the volume of a cylinder?
Q
A
rd
hr
When a sphere and a cylinder have the same radius, r, and the height, h, of the cylinder equals the diameter, d, of the sphere, they have the following relationship:
volume of sphere =
volume of sphere =
volume of sphere =
volume of sphere =
32 volume of
cylinder
4πr 3
3
(πr 2h)
(πr 2)(2r)
32
32
Chapter FAQ
1 Perimeter, Area, and Volume
Reveal
You have been asked to design one of the holes in a mini-golf game for a charity carnival.
Chapter 1 TaskDesigning Minigolf
Players who score a hole-in-one will win a prize, so the hole should not be easy!
1 Perimeter, Area, and Volume
DESIGN CRITERIA
• The hole must consist of a composite shape that contains at least three different shapes.• The obstacles on the hole must include at least three of these objects: cone, sphere (or hemisphere), cylinder, prism, pyramid.
Chapter 1 TaskDesigning Minigolf
1 Perimeter, Area, and Volume
MATERIALS AVAILABLE
• wooden rails for the borders of the hole
• Styrofoam for obstacles
• artificial turf for the floor
Chapter 1 TaskDesigning Minigolf
1 Perimeter, Area, and Volume
• detailed diagram of the hole, with dimensions• detailed description of the obstacles, with dimensions
• description of the materials needed to build the hole (wood, in metres; turf, in square metres; Styrofoam, in cubic metres)
REPORT CRITERIA
Chapter 1 TaskDesigning Minigolf
1 Perimeter, Area, and Volume