1. Calculate the exact volume of a cylinder with a radius of 5 cm and a height of 10 cm.

2. Find the volume of a cone that has a radius of 6 inches and a height of 8 inches.

3. Calculate the volume of a sphere with a radius of 3 meters.

4. A cylinder has a total volume of \( 160\pi \text{ cm}^3 \) and a height of 10 cm. Solve for the exact value of its radius (\( r \)).

5. The volume of a cone is \( 100\pi \text{ in}^3 \), and its base radius is 5 inches. Determine its height (\( h \)).

6. A solid hemisphere (half of a sphere) has a radius of 6 cm. What is its volume?

7. Calculate the volume of a sphere that has a diameter of 12 cm.

8. The circumference of the base of a cylinder is \( 10\pi \text{ cm} \). If the height is 8 cm, what is the exact volume?

9. A cone has a volume of \( 48\pi \text{ in}^3 \) and a height of 9 inches. What is the length of its radius?

10. Calculate the exact volume of a sphere with a radius of 9 units.

11. Calculate the Lateral Surface Area (LSA) of a cylinder with a radius of 4 m and a height of 10 m.

12. Determine the Total Surface Area (TSA) of a cylinder that has a radius of 3 cm and a height of 5 cm.

13. A rectangular prism has a base measuring 4 units by 5 units, and a height of 10 units. Find its Lateral Surface Area.

14. Find the Total Surface Area of a rectangular prism with dimensions 3 ft, 4 ft, and 5 ft.

15. A triangular prism has a right-triangular base with side lengths 3 cm, 4 cm, and 5 cm. If the height of the prism is 10 cm, compute the Lateral Surface Area.

16. Using the same triangular prism from the previous question (base sides 3, 4, 5 and height 10), what is its Total Surface Area?

17. Determine the Lateral Surface Area of a cylinder with a radius of 5 units and a height of 12 units.

18. Calculate the Total Surface Area of a cylinder that has a radius of 6 cm and a height of 4 cm.

19. A rectangular prism has a base measuring 6 in by 8 in, and a height of 5 in. What is its Total Surface Area?

20. A triangular prism has bases that are equilateral triangles with a side length of 6 cm. If the height of the prism is 10 cm, compute the Lateral Surface Area.

21. A right triangle has legs measuring 5 cm and 12 cm. Determine the exact length of the hypotenuse.

22. In a right triangle, the hypotenuse is 25 units long and one leg is 7 units long. What is the length of the other leg?

23. Calculate the direct distance between the points \( (1, 2) \) and \( (4, 6) \) on a coordinate plane.

24. What is the precise distance between the coordinates \( (-2, -3) \) and \( (3, 9) \)?

25. A rectangular television screen has a width of 15 inches and a height of 8 inches. What is the length of its diagonal?

26. A 20-foot ladder leans against a vertical building. The base of the ladder is placed exactly 12 feet away from the bottom of the wall. How high up the wall does the ladder reach?

27. A right triangle has a hypotenuse measuring 41 units and one leg measuring 9 units. Find the exact length of the other leg.

28. Calculate the exact distance between the coordinate points \( (-4, -5) \) and \( (4, 10) \).

29. A rectangular swimming pool has a width of 10 meters and a length of 24 meters. Determine the diagonal distance across the pool.

30. Find the direct straight-line distance from the origin \( (0,0) \) to the point \( (-12, 5) \).

31. Solve for \( x \): \( \quad 4x - 7 = 2x + 11 \)

32. Evaluate and solve for \( x \): \( \quad 3(x + 2) = 5x - 8 \)

33. Solve the fractional equation: \( \quad \frac{1}{2}x + 5 = \frac{1}{4}x + 9 \)

34. Solve for \( x \): \( \quad -2(3x - 1) = 4x + 22 \)

35. Combine like terms and solve: \( \quad 5x + 3 - 2x = x + 15 \)

36. Solve for \( x \): \( \quad 0.5(4x + 8) = 3x - 6 \)

37. Solve for \( x \): \( \quad 6x - 4(x - 2) = x + 15 \)

38. Solve the fractional equation: \( \quad \frac{2}{3}x - 4 = \frac{1}{3}x + 6 \)

39. Solve for \( x \): \( \quad -3(2x + 5) = -4x - 23 \)

40. Solve for \( x \): \( \quad 0.25(8x - 12) = 1.5x + 7 \)

41. Two parallel lines are cut by a transversal. Two alternate interior angles are represented by \( (3x + 10)^\circ \) and \( (5x - 20)^\circ \). Find the exact degree measure of these angles.

42. Two corresponding angles created by a transversal cutting parallel lines are \( (4x - 5)^\circ \) and \( (3x + 15)^\circ \). Solve for \( x \).

43. Two same-side (consecutive) interior angles measure \( (2x + 10)^\circ \) and \( (3x + 20)^\circ \). Compute the value of \( x \).

44. The exterior angle of a triangle measures \( 120^\circ \). The two remote (opposite) interior angles measure \( x^\circ \) and \( (2x)^\circ \). Calculate the measure of the larger of these two remote interior angles.

45. Two parallel lines are intersected by a transversal. Two alternate exterior angles measure \( (7x - 12)^\circ \) and \( (4x + 24)^\circ \). Find the value of \( x \).

46. Two angles form a linear pair (supplementary on a straight line). Their measures are \( 5x^\circ \) and \( (3x + 20)^\circ \). What is the exact measure of the larger angle?

47. Two same-side (consecutive) interior angles measure \( (4x + 15)^\circ \) and \( (2x + 45)^\circ \). What is the exact measure of the smaller angle?

48. Two intersecting lines form vertical angles represented by \( (3x - 12)^\circ \) and \( (x + 36)^\circ \). Calculate the measure of these vertical angles.

49. Two angles form a linear pair. Their measures are \( (2x)^\circ \) and \( (7x - 18)^\circ \). Solve for \( x \).

50. Two parallel lines are intersected by a transversal. The alternate interior angles are \( (5x - 10)^\circ \) and \( (2x + 35)^\circ \). Solve for \( x \).