Unit 3 Review

Front

What is the formula for the volume of a cone?

Back

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

Front

How do you calculate the diameter of a cylinder given its volume and height?

Back

To find the diameter of a cylinder, use the formula V = πr²h to solve for r, then multiply by 2 to get the diameter: d = 2r.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Front

What is the slant height of a cone?

Back

The slant height (l) of a cone can be found using the formula l = √(r² + h²), where r is the radius and h is the height.

Front

What defines a Pythagorean triple?

Back

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c².

Front

How do you find the height of a cone if you know the volume and radius?

Back

Rearrange the volume formula V = (1/3)πr²h to solve for h: h = (3V)/(πr²).

Front

What is the relationship between the radius and diameter of a circle?

Back

The diameter of a circle is twice the radius: d = 2r.

Front

How can you determine if a triangle is a right triangle using side lengths?

Back

If the square of the longest side equals the sum of the squares of the other two sides, then it is a right triangle (Pythagorean theorem).

Front

What is the formula for the volume of a cylinder?

Back

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

Front

How do you calculate the area of a triangle given its side lengths?

Back

You can use Heron's formula: A = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (s = (a+b+c)/2) and a, b, c are the side lengths.