Area & Volume - SAT Math

1. State the formula for the volume of a rectangular prism.

   $Volume = length \times width \times height$. Multiply all three dimensions together.

2. What is the formula for the volume of a prism?

   Volume = base area × height. Base area times perpendicular height.

3. Identify the formula for the surface area of a cube.

   Surface Area = $6 \times \text{side}^2$. Six faces, each with area of $\text{side}^2$.

4. Identify the formula for the volume of a rectangular prism.

   Volume = length × width × height. Product of all three dimensions.

5. What is the formula for the surface area of a sphere?

   Surface Area = 4πr². Four times the area of a great circle.

6. Calculate the area of a triangle with base 10 and height 6.

   Area = 30. Using $\frac{1}{2} \times 10 \times 6 = 30$.

7. What is the formula for the area of a triangle?

   Area = $\frac{1}{2}$ × base × height. Half the product of base and height.

8. State the formula for the area of a sector of a circle.

   Area = $\frac{\theta}{360} \times \pi r^2$. Fraction of full circle based on central angle.

9. State the formula for the volume of a cylinder.

   Volume = $\pi r^2 h$. Base area times height: $\pi r^2 \times h$.

10. What is the formula for the area of a circle?

    Area = $\pi r^2$. $\pi$ times the square of the radius.

11. Calculate the surface area of a rectangular prism with dimensions 2, 3, 4.

    Surface Area = 52. Using $2(2 \times 3 + 2 \times 4 + 3 \times 4) = 52$.

12. What is the formula for the area of a rectangle?

    $Area = length \times width$. Multiply the two perpendicular sides of the rectangle.

13. Find the surface area of a sphere with radius 3.

    Surface Area = 36π. Using $4\pi \times 3^2 = 36\pi$.

14. What is the formula for the volume of a cube?

    Volume = $side^3$. Side length cubed for equal dimensions.

15. What is the surface area of a cylinder with radius 2 and height 5?

    Surface Area = 28π. Using $2\pi \times 2(5 + 2) = 28\pi$.

16. What is the lateral surface area of a cylinder with radius 4 and height 10?

    Lateral Surface Area = 80π. Using $2\pi \times 4 \times 10 = 80\pi$.

17. Identify the formula for the surface area of a cone.

    Surface Area = $\pi r(r + l)$. Base area plus lateral surface area.

18. Calculate the volume of a cube with side length 3.

    Volume = 27. Cube the side length: $3^3 = 27$.

19. Find the volume of a cylinder with radius 3 and height 7.

    Volume = 63π. Using $\pi \times 3^2 \times 7 = 63\pi$.

20. Identify the formula for the area of a parallelogram.

    Area = base × height. Same as rectangle when base and height are perpendicular.

21. State the formula for the circumference of a circle.

    Circumference = 2πr. Two times pi times radius.

22. State the formula for the surface area of a cylinder.

    Surface Area = $2\pi r (h + r)$. Two circular bases plus lateral surface area.

23. Calculate the area of a trapezoid with bases 6 and 8, height 4.

    Area = 28. Using $\frac{1}{2} \times (6 + 8) \times 4 = 28$.

24. Calculate the volume of a cone with radius 4 and height 9.

    Volume = 48π. Using $\frac{1}{3}\pi \times 4^2 \times 9 = 48\pi$.

25. State the formula for the area of a trapezoid.

    $ \text{Area} = \frac{1}{2} \times ($base_1$ + $base_2$) \times height $. Average of parallel bases times height.

26. State the formula for the volume of a cylinder.

    Volume = $\pi r^2 h$. Base area times height for circular cross-section.

27. What is the area of a circle with radius 5?

    Area = $25\pi$. Using $\pi \times 5^2 = 25\pi$.

28. Identify the formula for the lateral surface area of a cylinder.

    Lateral Surface Area = 2πrh. Only the curved side surface, excluding bases.

29. Identify the formula for the volume of a sphere.

    $Volume = \frac{4}{3} \times πr^3$. Four-thirds times $\pi$ times radius cubed.

30. Calculate the surface area of a cone with radius 3 and slant height 5.

    Surface Area = 24π. Using $\pi \times 3(3 + 5) = 24\pi$.

31. Calculate the volume of a cube with side length 4.

    Volume = 64. Using $4^3 = 64$.

32. What is the formula for the area of a parallelogram?

    $Area = base \times height$. Base times the perpendicular height to that base.

33. State the formula for the volume of a sphere.

    Volume = $\frac{4}{3} \pi r^3$. Four-thirds pi times radius cubed.

34. What is the volume of a rectangular prism with dimensions 3, 4, 5?

    Volume = 60. Using $3 \times 4 \times 5 = 60$.

35. What is the volume of a sphere with radius 6?

    Volume = 288π. Using $\frac{4}{3}\pi \times 6^3 = 288\pi$.

36. What is the formula for the volume of a cone?

    Volume = $\frac{1}{3} \pi r^2 h$. One-third of cylinder volume with same base and height.

37. Determine the area of a circle with radius 5.

    Area = 25π. Use $\pi r^2$: $\pi \times 5^2 = 25\pi$.

38. State the formula for the area of a rectangle.

    Area = length × width. The fundamental formula for rectangular area.

39. Find the circumference of a circle with radius 7.

    Circumference = 14π. Using $2\pi \times 7 = 14\pi$.

40. What is the area formula for a triangle?

    $Area = \frac{1}{2} \times base \times height$. Half the product of base and perpendicular height.

41. Calculate the area of a sector with radius 6 and angle 60°.

    Area = $6\pi$. Using $\frac{60}{360} \times \pi \times 6^2 = 6\pi$.

42. Find the volume of a pyramid with base area 10 and height 6.

    Volume = 20. Using $\frac{1}{3} \times 10 \times 6 = 20$.

43. What is the formula for the surface area of a rectangular prism?

    Surface Area = 2lw + 2lh + 2wh. Sum of areas of all six rectangular faces.

44. What is the formula for the volume of a pyramid?

    Volume = $\frac{1}{3}$ × base area × height. One-third of prism volume with same base and height.

45. Find the area of a rectangle with length 8 and width 5.

    Area = 40. Using $8 \times 5 = 40$.

46. Calculate the volume of a prism with base area 15 and height 8.

    Volume = 120. Using $15 \times 8 = 120$.

47. Find the surface area of a cube with side length 5.

    Surface Area = 150. Using $6 \times 5^2 = 150$.

48. What is the formula for the area of a circle?

    Area = πr². Pi times radius squared.

49. Find the area of a parallelogram with base 7 and height 3.

    Area = 21. Using $7 \times 3 = 21$.

50. Find the area of a square with side length 4.

    Area = 16. Square the side length: $4^2 = 16$.

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