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

What is the formula to find the length of the diagonal in a rectangular prism?

Back

The length of the diagonal (d) in a rectangular prism can be found using the formula: d = √(l² + w² + h²), where l is the length, w is the width, and h is the height.

Front

How do you find the height of a cone using the Pythagorean Theorem?

Back

To find the height (h) of a cone, use the formula: h = √(s² - (r)²), where s is the slant height and r is the radius of the base.

Front

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

Back

The diameter (d) of a circle is twice the radius (r). This can be expressed as: d = 2r.

Front

If the area of a square base is 144 square feet, what is the length of one side?

Back

The length of one side (s) of a square can be found using the formula: s = √(area). Therefore, s = √(144) = 12 feet.

Front

What is the slant height of a pyramid?

Back

The slant height (l) of a pyramid is the distance from the apex (top point) of the pyramid to the midpoint of one of the sides of the base.

Front

How do you calculate 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 = √(l² - (s/2)²), where l is the slant height and s is the length of a side of the base.

Front

What is the approximate value of √(3) to three decimal places?

Back

The approximate value of √(3) is 1.732.

Front

In a right triangle, if one leg is 3 and the other leg is 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 3² + 4², c² = 9 + 16, c² = 25, so c = 5.

Front

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

Back

The volume (V) of a rectangular prism is calculated using the formula: V = l × w × h, where l is the length, w is the width, and h is the height.