Pythagorean Theorem 3D Shapes

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). It can be expressed as: c² = a² + b².

Front

How do you find the height of a pyramid given the area of the base and the slant height?

Back

To find the height (h) of a pyramid, use the formula: h = √(slant height² - (base side length/2)²). First, calculate the base side length from the area, then apply the formula.

Front

What is the formula for the diagonal of a rectangular prism?

Back

The formula for the diagonal (d) of a rectangular prism is: d = √(length² + width² + height²).

Front

How do you calculate the area of a square base?

Back

The area (A) of a square base is calculated using the formula: A = side length².

Front

What is the relationship between the slant height, height, and base of a pyramid?

Back

In a pyramid, the slant height, height, and half the base length form a right triangle, allowing the use of the Pythagorean Theorem to find unknown dimensions.

Front

What is the height of a cone if the radius is known?

Back

The height (h) of a cone can be found using the formula: h = √(slant height² - radius²).

Front

How do you find the length of the diagonal in a 3D shape?

Back

To find the length of the diagonal in a 3D shape, use the formula: diagonal = √(length² + width² + height²).

Front

What is the formula for the volume of a pyramid?

Back

The volume (V) of a pyramid is calculated using the formula: V = (1/3) × base area × height.

Front

What is the formula for the volume of a cone?

Back

The volume (V) of a cone is calculated using the formula: V = (1/3) × π × radius² × height.

Front

How do you determine the dimensions of a swimming pool using the Pythagorean Theorem?

Back

To determine the dimensions of a swimming pool, use the Pythagorean Theorem to relate the lengths of the sides and the diagonal.