Circles
What is the radius of a circle?
The radius is the distance from the center of the circle to any point on its circumference.
Volume is the amount of three-dimensional space an object occupies
It is measured in cubic units (e.g., cm³, m³).
What are the main types of geometric transformations?
Translation – moving a shape without rotating or resizing it.
Rotation – turning a shape around a fixed point.
Reflection – flipping a shape over a line (mirror image).
Dilation – resizing a shape either larger or smaller, maintaining proportions.
A rectangle has a length of 12 cm and a width of 5 cm. What is its perimeter?
Perimeter = 2 × (Length + Width)
= 2 × (12 + 5) = 2 × 17 = 34 cm
What is the Mean?
The mean is the average. You add all the numbers together and divide by how many numbers there are.
What is the diameter of a circle?
The diameter is twice the length of the radius and passes through the center of the circle.
Volume=a3
Where a is the length of a side of the cube.
What is the result of reflecting a point (3, 4) over the y-axis?
(–3, 4)
What is the area of a triangle with a base of 10 cm and a height of 6 cm?
Area = ½ × base × height
= ½ × 10 × 6 = 30 cm²
What is the Median?
the median is the middle number when the numbers are in order.
What is the formula for the circumference of a circle?
Circumference = 2πr2\pi r2πr, where rrr is the radius.
Volume=l×w×h
Where l is length, w is width, and h is height.
Describe the effect of a 90° clockwise rotation about the origin on the point (x, y).
A 90° clockwise rotation about the origin changes (x, y) to (y, –x).
A circle has a radius of 7 cm. What is its circumference? (Use π ≈ 3.14)
Circumference = 2 × π × radius
= 2 × 3.14 × 7 = 43.96 cm
What is the Range?
The range is the difference between the biggest and smallest numbers.
: What is the formula for the area of a circle?
Area = πr2pi r^2πr2, where r is the radius.
Volume=πr2h
Where r is the radius of the base, and h is the height.
If a triangle has vertices A(1, 2), B(4, 2), and C(3, 5), what are the coordinates after translating the triangle by the vector (–2, 3)?
A becomes: (1 – 2, 2 + 3) = (–1, 5)
B becomes: (4 – 2, 2 + 3) = (2, 5)
C becomes: (3 – 2, 5 + 3) = (1, 8)
What is the area of a circle with a radius of 4 cm? (Use π ≈ 3.14)
Area = π × radius²
= 3.14 × 4² = 3.14 × 16 = 50.24 cm²
What is the Mode?
The mode is the number that appears the most.
What is a chord?
A chord is a line segment whose endpoints lie on the circle.
Volume=4/3πr3
Where r is the radius.
What is a dilation, and how does it affect a shape?
If scale factor > 1 → shape enlarges
If 0 < scale factor < 1 → shape shrinks
What is the perimeter of a square with one side measuring 9 cm
Perimeter = 4 × side
= 4 × 9 = 36 cm
What is a Two-Way Table?
A two-way table shows data that compares two things at once.