The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

The volume of a cylinder is πr²h:

v = πr²h
v = π(1² x 1)
v = 1π

You need to find the value of b so solve the first equation in terms of z:

4b + z = 4
z = 4 - 4b

then substitute the result (4 - 4b) into the second equation:

4b - 5(4 - 4b) = 4
4b + (-5 x 4) + (-5 x -4b) = 4
4b - 20 + 20b = 4
4b + 20b = 4 + 20
24b = 24
b = \( \frac{24}{24} \)
b = 1

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

The formula for area is πr². Radius is circle \( \frac{diameter}{2} \):

r = \( \frac{d}{2} \)
r = \( \frac{4}{2} \)
r = 2
a = πr²
a = π(2²)
a = 4π