Pythagorean Theorem and Volume

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: a² + b² = c².

Front

How do you determine if a triangle is a right triangle?

Back

A triangle is a right triangle if it satisfies the Pythagorean Theorem: a² + b² = c², where c is the longest side.

Front

What is the formula for the volume of a cylinder?

Back

The volume (V) of a cylinder can be calculated using the formula: V = πr²h, where r is the radius and h is the height.

Front

If a triangle has sides of lengths 9 cm, 40 cm, and 41 cm, is it a right triangle?

Back

Yes, it is a right triangle because 9² + 40² = 41² (81 + 1600 = 1681).

Front

What is the length of the diagonal of a rectangle with width 90 m and length 120 m?

Back

The diagonal can be found using the Pythagorean Theorem: d = √(90² + 120²) = √(8100 + 14400) = √22500 = 150 m.

Front

What is the height of a cylinder with a volume of 502.4 cm³ and a radius of 4 cm?

Back

Using the volume formula V = πr²h, we can rearrange to find h: h = V / (πr²). Thus, h = 502.4 / (π * 4²) = 10 cm.

Front

What does it mean for a triangle to be scalene?

Back

A scalene triangle is a triangle in which all three sides have different lengths.

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, where the shortest side is opposite the 30° angle.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

How do you find the area of a right triangle?

Back

The area (A) of a right triangle can be calculated using the formula: A = (1/2) * base * height.