Circular Reasoning
Complicating Shapes
Increasing the Volume
Bipeds, Quadripeds and More
100
Find the Radius, Diameter, and Area of the circle below.
r = 7
d = 14
a = 49Ï€
100
Find the following shape on your paper. What is its area?
6x9 = 54
6x9 = 54
6x9x(1/2) = 27
3x9x(1/2) = 13.5
54 + 54 + 27 + 13.5 = 148.5
100
Find the volume of the cube below.
Each face has 16 cubes. There are 4 sides stacked to form a total of 4x16 = 64
100
What does the quadra in quadrilateral mean?
*bonus 100 pts, what makes an animal a hexaped?
quad is latin for 4. A quadri - lateral has 4 sides
hexa is latin for 6. So a hexa - ped (think pedals) has 6 legs.
200
Triet runs around the world and measures it to have a circumference of 25k mi.
He then digs a hole straight through the center of the earth, from Peru to Vietnam. It's about 8k miles.
What circle-related term describes the number 8k?
What is the (proportional) relationship between 8k and the circumference?
8k is the diameter of the earth.
The proportional relationship between circumference and diameter is that circumference/diameter = 3.14...
200
How many sides does the cube have? What is its surface area?
fun fact: each little piece is called a cubelet.
It has 6 sides. 2 blue, 2 red, 2 yellow.
Each side is the same size (4x4 = 16).
So if I multiply the area of each side by 6 I get the total surface area. 6 x 16 = 96 cubelets.
200
Sketch a cross section parallel to the base. What is the area of the shape you've sketched?
area = 10 + 8 = 18 square cm
200
How long/short could the missing side of this triangle be? Remember spaghetti noodles.
It cannot be bigger than or equal to 8+6 = 14
It cannot be smaller than 8-6 = 2
The missing side is...
2 < missing side < 14
300
Circle A has a radius of 2.
Circle B has an area of 16Ï€.
Circle C has a diameter of 7.
Rank the 3 from largest to smallest.
Choose 1 trait to compare. (radius, diameter, etc...)
Radius A = 2
Radius B --> a = pir^2 = π x 16 =
Ï€ x 4^2 --> r = 4
Radius C = 7/2 = 3.5
B, C, A
300
Check your paper for a shape that matches mine.
The area of the circle as a whole will have a radius of 12 + 13 = 25 --> pir^2 = 625Ï€
Then we need to subtract the area of the smaller circle which is again, pir^2 . But this time our r = 13. So, pix13x13 =169Ï€
To find the shaded region we subtract 625Ï€ and 169Ï€ to get 456Ï€ which is our area.
300
The solid below is on your paper. What is its volume?
The cylinder has a base of 16Ï€ and a height of 8 so its area will be 16Ï€ x 8 = 128Ï€ cubic ft
The rectangle has an area of l x w x h = 14 x 8 x 12 = 1,344 cubic ft
In total the volume is 1,344 + 128Ï€ cubic ft
300
You have a graph on your packet paper. Use it to construct a parallelogram 3 units tall and 5 units wide. One of the points must be on the origin (0,0).
