Math III EOC Review #1

Front

What is the standard form of a circle's equation?

Back

The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

How do you find the radius of a circle from its equation?

Back

To find the radius, rewrite the circle's equation in standard form and identify r from (x - h)² + (y - k)² = r².

Front

What is the center of a circle in the equation x² + y² - 8x + 10y - 8 = 0?

Back

The center is (4, -5).

Front

What is the formula for the volume of a cone?

Back

The volume V of a cone is given by V = (1/3)πr²h, where r is the radius and h is the height.

Front

Calculate the volume of a cone with a diameter of 8 cm and height of 18 cm.

Back

The volume is 96π cm³.

Front

What is the formula for the volume of a cylinder?

Back

The volume V of a cylinder is V = πr²h, where r is the radius and h is the height.

Front

If the volume of a cylinder is 150 in³ and the radius is 4 in, how do you find the height?

Back

Use the formula h = V / (πr²). For this cylinder, h = 150 / (π * 4²) = 3 inches.

Front

What is a centroid in a triangle?

Back

The centroid is the point where the three medians of a triangle intersect.

Front

What are medians in a triangle?

Back

Medians are line segments that connect a vertex of the triangle to the midpoint of the opposite side.

Front

What is the difference between the centroid and circumcenter of a triangle?

Back

The centroid is the intersection of the medians, while the circumcenter is the intersection of the perpendicular bisectors of the sides.