Volume & Pythagorean Theorem Review

Front

What is the formula for the volume of a sphere?

Back

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

Front

If the radius of a sphere is doubled, how does the volume change?

Back

If the radius is doubled, the volume increases by a factor of 8.

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

How do you find the distance traveled using the Pythagorean Theorem?

Back

To find the distance traveled in a right triangle, use the Pythagorean Theorem: distance = √(a² + b²), where a and b are the lengths of the two legs.

Front

What is the volume of a sphere with a radius of 2 feet?

Back

Using the formula V = (4/3)π(2)³, the volume is approximately 33.51 ft³.

Front

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

Back

The diameter of a sphere is twice the radius: diameter = 2 × radius.

Front

What is the square root of a number?

Back

The square root of a number x is a value that, when multiplied by itself, gives x. It is denoted as √x.

Front

How do you calculate the volume of a cylinder?

Back

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

Front

What is the volume of a cylinder with a radius of 3 feet and a height of 5 feet?

Back

Using the formula V = π(3)²(5), the volume is approximately 141.37 ft³.

Front

What is the formula for the area of a circle?

Back

The area A of a circle is given by the formula A = πr², where r is the radius.