Volume & Pythagorean Theorem Review

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). Formula: a² + b² = c².

Front

What is the formula for the volume of a sphere?

Back

The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere.

Front

How do you find the volume of a cylinder?

Back

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

Front

What is 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 of the base and h is the height of the cone.

Front

Identify the hypotenuse in a right triangle with sides 5, 12, and 13.

Back

The hypotenuse is 13, as it is the longest side in a right triangle.

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem applies only to right triangles.

Front

If a right triangle has legs of lengths 6 and 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10.

Front

What is the volume of a cube with a side length of 4 cm?

Back

The volume of a cube is V = s³; V = 4³ = 64 cm³.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

How do you calculate the area of a triangle?

Back

The area of a triangle is calculated using the formula A = (1/2)bh, where b is the base and h is the height.