A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r²h and the surface area is 2(π r²) + 2π rh.

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with b° = 149, the value of a° is 31.

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(2²) + 2π(2 x 4)
sa = 2π(4) + 2π(8)
sa = (2 x 4)π + (2 x 8)π
sa = 8π + 16π
sa = 24π

The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):

sa = 2lw + 2wh + 2lh
sa = (2 x 8 x 7) + (2 x 7 x 4) + (2 x 8 x 4)
sa = (112) + (56) + (64)
sa = 232

To solve this equation, isolate the variable for which you are solving (b) on one side of the equation and put everything else on the other side.

2b + 5z = -b - 9z + 2
2b = -b - 9z + 2 - 5z
2b + b = -9z + 2 - 5z
3b = -14z + 2
b = \( \frac{-14z + 2}{3} \)
b = \( \frac{-14z}{3} \) + \( \frac{2}{3} \)
b = -4\(\frac{2}{3}\)z + \(\frac{2}{3}\)