Circles & Spheres
Define the circumference of a circle.
The circumference is the perimeter of a circle.
Define a segment.
A line segment is part of a straight line bounded by two distinct endpoints.
Draw or describe a pair of supplementary angles.
Supplementary angles are a pair of angles that add up to 180 degrees, forming a straight line.
Draw an example of an acute angle.
An angle that measures less than 90 degrees.
When is Ms. Drager getting married?
June 24th
Find the area of a circle with a diameter of 15 inches.
a = pi x r^2 --> 3.14 x 7.5 x 7.5
= 176.625 inches^2
Find the slope of line AB:
A (-2, -3)
B (-4, -7)
Slope = 2
Angle ABC with a measure of 134 degrees is bisected by ray BD. What is the measure of angle ABD?
134 / 2 = 67 degrees
Describe or draw an example of collinear points.
Triangle MNO in quadrant 1 is reflected over the line y=x and then rotated 90 degrees counterclockwise to produce triangle PQR. What quadrant is triangle PQR located in?
Quadrant 1 --> Quadrant 1 --> Quadrant 2
Quadrant 2
SEE BOARD:
What percentage of a circle is the sector with a radius of 8cm and a 40-degree angle?
40 / 360 = 1 / 9 = 0.11 x 100
= 11.11%
Find the midpoint between points A (-3, 7) and B (5, -1)
midpoint = (x + x / 2, y + y / 2)
= [(-3 + 5 / 2), (7 + -1 / 2)]
= (1, 3)
A circle has an inscribed angle and a center angle. The angle at the center of the circle is 98 degrees. What is the measure of the inscribed angle?
98 / 2 = 49 degrees
Describe or draw a chord.
A chord is a line segment connecting two points on a curve, usually on a circle. It does NOT go through the center of the circle.
Jeremy wants to know the density of a rock in grams per cubic centimeter. The rock has a mass of 1.08 kilograms and a volume of 400 cubic centimeters. What is the density of the rock, in GRAMS per cubic centimeter?
1.08 kg * 1000 g/kg = 1,080 grams
1,080 grams / 400 cubic cm = 2.7 grams /cubic cm
Find the volume of a hemisphere with a diameter of 11.5 cm.
1) v = 2/3 x pi x r^3
2) find the radius: 11.5 / 2 = 5.75 cm
3) plug in and get: 397.96 cm^3
Find the slope of the line PERPENDICULAR to line CD:
C (3, -4)
D (6, -9)
1) Find slope of CD: -5/3
2) Take the opposite reciprocal of CD slope
= 3/5
Given that an isosceles triangle has one angle with a measure of 28 degrees, find the other two angles in the triangle.
180 - 28 = 152 / 2 = 76 degrees
Explain the difference between congruent and equal. (Define or draw an example for each).
If all parts of a pair of shapes are the same size or measure, then they are said to be congruent. When comparing a shape to itself, we can use the term equal.
The equation of a line is 6x - 3y = 5. Find the slope of a line perpendicular to the line.
Slope = 2 --> opposite reciprocal = -1/2 slope of the perpendicular line
Baseballs and basketballs are known to be spheres. The diameter of a given basketball is 10 inches. The volume of a specific baseball is 2.7% of the volume of the given basketball. Find the radius of the baseball.
1) Find the volume of the basketball
2) Find the volume of the baseball (basketball * 0.27)
3) Find the radius of the baseball = 1.5 cm
Line k has a slope of -5. Line j is perpendicular to line k and passes through the point (5, 9). Create the equation for line j.
y = mx + b --> 9 = (1/5)*5 + b --> 9 = 1 + b
y = 1/5x + 8
SEE THE BOARD:
Given that the measure of angle 3 is 65 degrees, find the measure of angle 8.
The measure of angle 8 = 115 degrees
Explain the difference between congruent and corresponding. (Define or draw an example for each).
Congruent figures are identical in size, shape, and measure. The corresponding sides and angles between two triangles are sides or angles in the same relative position.
Kayla is picking fruit from a basket that contains different types of fruits. Which set of events is independent?
a) event 1: she picks a kiwi and eats it, event 2: she picks an apple and eats it
b) event 1: she picks an apple and eats it, event 2: she picks an apple and puts it back
c) event 1: she picks a kiwi and puts it back, event 2: she picks an apple and puts it back
C) Since she puts the kiwi back after the first pick, the same amount of fruit remains, and each event does not effect the other one.