SAT Math Flashcards: Area And Volume

What this deck covers

This deck focuses on Area And Volume, giving you a quick way to review the definitions, rules, and examples that matter most for SAT Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the formula for the surface area of a sphere?

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

Flashcard 2: Calculate the area of a trapezoid with bases 6 and 8, height 4.

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

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

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

Flashcard 4: Calculate the surface area of a cone with radius 3 and slant height 5.

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

Flashcard 5: State the formula for the volume of a rectangular prism.

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

Flashcard 6: What is the formula for the volume of a pyramid?

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

Flashcard 7: What is the formula for the volume of a prism?

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

Flashcard 8: Identify the formula for the surface area of a cube.

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

Flashcard 9: What is the formula for the volume of a cone?

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

Flashcard 10: Identify the formula for the surface area of a cube.

Answer: Surface Area = 6 × $side^2$. Six faces, each with area of $side^2$.

Flashcard 11: Identify the formula for the volume of a rectangular prism.

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

Flashcard 12: What is the formula for the surface area of a sphere?

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

Flashcard 13: Calculate the volume of a cone with radius 4 and height 9.

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

Flashcard 14: State the formula for the volume of a cylinder.

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

Flashcard 15: Calculate the area of a triangle with base 10 and height 6.

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

Flashcard 16: What is the volume of a sphere with radius 6?

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

Flashcard 17: What is the formula for the area of a triangle?

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

Flashcard 18: State the formula for the area of a sector of a circle.

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

Flashcard 19: State the formula for the volume of a cylinder.

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

Flashcard 20: What is the formula for the area of a circle?

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

Flashcard 21: Calculate the surface area of a rectangular prism with dimensions 2, 3, 4.

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

Flashcard 22: Calculate the area of a sector with radius 6 and angle 60°.

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

Flashcard 23: What is the formula for the volume of a cube?

Answer: Volume = side³. Side length cubed for equal dimensions.

Flashcard 24: What is the formula for the area of a rectangle?

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

Flashcard 25: Find the surface area of a sphere with radius 3.

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

Flashcard 26: What is the formula for the volume of a cube?

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

Flashcard 27: State the formula for the area of a trapezoid.

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

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

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

Flashcard 29: What is the surface area of a cylinder with radius 2 and height 5?

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

Flashcard 30: Find the circumference of a circle with radius 7.

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

Flashcard 31: What is the lateral surface area of a cylinder with radius 4 and height 10?

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

Flashcard 32: Identify the formula for the area of a parallelogram.

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

Flashcard 33: What is the area of a circle with radius 5?

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

Flashcard 34: What is the formula for the volume of a prism?

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

Flashcard 35: State the formula for the volume of a sphere.

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

Flashcard 36: Find the surface area of a cube with side length 5.

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

Flashcard 37: Identify the formula for the surface area of a cone.

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

Flashcard 38: Calculate the volume of a cube with side length 3.

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

Flashcard 39: Calculate the volume of a cube with side length 3.

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

Flashcard 40: What is the formula for the area of a circle?

Answer: Area = πr². Pi times radius squared.

Flashcard 41: State the formula for the area of a rectangle.

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

Flashcard 42: Find the volume of a cylinder with radius 3 and height 7.

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

Flashcard 43: Identify the formula for the area of a parallelogram.

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

Flashcard 44: Find the surface area of a sphere with radius 3.

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

Flashcard 45: Identify the formula for the surface area of a cone.

Answer: Surface Area = $πr(r + l)$. Base area plus lateral surface area.

Flashcard 46: State the formula for the circumference of a circle.

Answer: Circumference = $2\pi r$. Two times pi times radius.

Flashcard 47: State the formula for the circumference of a circle.

Answer: Circumference = 2πr. Two times pi times radius.

Flashcard 48: State the formula for the surface area of a cylinder.

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

Flashcard 49: Calculate the area of a trapezoid with bases 6 and 8, height 4.

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

Flashcard 50: Calculate the volume of a cone with radius 4 and height 9.

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

Flashcard 51: State the formula for the area of a trapezoid.

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

Flashcard 52: State the formula for the area of a sector of a circle.

Answer: Area = $\frac{\theta}{360}$ × πr². Fraction of full circle based on central angle.

Flashcard 53: State the formula for the volume of a cylinder.

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

Flashcard 54: What is the area of a circle with radius 5?

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

Flashcard 55: Identify the formula for the lateral surface area of a cylinder.

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

Flashcard 56: Identify the formula for the volume of a sphere.

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

Flashcard 57: Calculate the area of a triangle with base 10 and height 6.

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

Flashcard 58: Calculate the surface area of a cone with radius 3 and slant height 5.

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

Flashcard 59: Find the area of a rectangle with length 8 and width 5.

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

Flashcard 60: Calculate the volume of a cube with side length 4.

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

Flashcard 61: What is the formula for the area of a parallelogram?

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

Flashcard 62: State the formula for the volume of a sphere.

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

Flashcard 63: What is the volume of a rectangular prism with dimensions 3, 4, 5?

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

Flashcard 64: Find the volume of a pyramid with base area 10 and height 6.

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

Flashcard 65: Find the area of a parallelogram with base 7 and height 3.

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

Flashcard 66: What is the volume of a sphere with radius 6?

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

Flashcard 67: State the formula for the volume of a rectangular prism.

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

Flashcard 68: What is the formula for the surface area of a rectangular prism?

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

Flashcard 69: Calculate the surface area of a rectangular prism with dimensions 2, 3, 4.

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

Flashcard 70: What is the volume of a rectangular prism with dimensions 3, 4, 5?

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

Flashcard 71: Determine the area of a circle with radius 5.

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

Flashcard 72: What is the formula for the area of a triangle?

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

Flashcard 73: Identify the formula for the volume of a rectangular prism.

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

Flashcard 74: What is the formula for the volume of a cone?

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

Flashcard 75: Determine the area of a circle with radius 5.

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

Flashcard 76: State the formula for the area of a rectangle.

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

Flashcard 77: What is the area formula for a triangle?

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

Flashcard 78: Find the circumference of a circle with radius 7.

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

Flashcard 79: Calculate the volume of a prism with base area 15 and height 8.

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

Flashcard 80: What is the area formula for a triangle?

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

Flashcard 81: State the formula for the surface area of a cylinder.

Answer: Surface Area = 2πr(h + r). Two circular bases plus lateral surface area.

Flashcard 82: Calculate the area of a sector with radius 6 and angle 60°.

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

Flashcard 83: Calculate the volume of a cube with side length 4.

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

Flashcard 84: Find the volume of a pyramid with base area 10 and height 6.

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

Flashcard 85: What is the formula for the surface area of a rectangular prism?

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

Flashcard 86: What is the formula for the volume of a pyramid?

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

Flashcard 87: What is the lateral surface area of a cylinder with radius 4 and height 10?

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

Flashcard 88: Find the area of a rectangle with length 8 and width 5.

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

Flashcard 89: Calculate the volume of a prism with base area 15 and height 8.

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

Flashcard 90: What is the surface area of a cylinder with radius 2 and height 5?

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

Flashcard 91: What is the formula for the area of a parallelogram?

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

Flashcard 92: State the formula for the volume of a cylinder.

Answer: Volume = πr²h. Base area times height for circular cross-section.

Flashcard 93: Find the surface area of a cube with side length 5.

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

Flashcard 94: What is the formula for the area of a circle?

Answer: Area = πr². Pi times radius squared.

Flashcard 95: Find the area of a parallelogram with base 7 and height 3.

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

Flashcard 96: Find the area of a square with side length 4.

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

Flashcard 97: What is the formula for the area of a circle?

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