PSAT 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 PSAT 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: State the formula for the volume of a cone with radius $r$ and height $h$.

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

Flashcard 2: Identify the volume of a cylinder with radius $3$ and height $5$.

Answer: $45\pi$. Using $V=\pi r^2h$ with $r=3$ and $h=5$.

Flashcard 3: Find the volume of a cylinder with radius $r=2$ and height $h=5$ in terms of $\pi$.

Answer: $20\pi$. Apply $V = \pi r^2h$: $\pi(2)^2(5) = 20\pi$.

Flashcard 4: What is the area of a rectangle with $l=9$ and $w=4$?

Answer: $36$. Apply $A = lw$: $9 \times 4 = 36$.

Flashcard 5: Find the area of a rectangle with $l=9$ and $w=4$.

Answer: $36$. Apply $A = lw$: $9 \times 4 = 36$.

Flashcard 6: What is the surface area formula for a rectangular prism with dimensions $l,w,h$?

Answer: $SA=2(lw+lh+wh)$. Sum of all six rectangular face areas.

Flashcard 7: What is the volume formula for a rectangular prism with dimensions $l,w,h$?

Answer: $V=lwh$. Multiply all three dimensions for box volume.

Flashcard 8: State the formula for the area of a triangle with base $b$ and height $h$.

Answer: A = rac{1}{2}bh. Half the product of base and height gives triangular area.

Flashcard 9: What is the surface area formula for a sphere with radius $r$?

Answer: $SA=4\pi r^2$. Four times pi times radius squared.

Flashcard 10: What is the area of a square with side length $s$?

Answer: $A = s^2$. Square area equals side length squared.

Flashcard 11: State the formula for the area of a trapezoid with bases $b_1, b_2$ and height $h$.

Answer: A = rac{1}{2}(b_1+b_2)h. Average of parallel bases times height.

Flashcard 12: Find the area of a circle with radius $r=3$ in terms of $\pi$.

Answer: $9\pi$. Apply $A = \pi r^2$: $\pi(3)^2 = 9\pi$.

Flashcard 13: What is the area of a circle with diameter $10$?

Answer: $25\pi$. Radius is $5$, so area is $\pi(5)^2 = 25\pi$.

Flashcard 14: State the formula for the surface area of a sphere with radius $r$.

Answer: $\text{SA} = 4\pi r^2$. Sphere surface area equals four times circle area with same radius.

Flashcard 15: State the formula for the area of a sector with radius $r$ and central angle $\theta$ degrees.

Answer: $A = \frac{\theta}{360}\pi r^2$. Fraction of circle's area based on angle ratio.

Flashcard 16: What is the volume of a sphere with $r=3$? (Leave in terms of $\pi$.)

Answer: $36\pi$. Apply $V = \frac{4}{3}\pi r^3$: $\frac{4}{3} \times \pi \times 3^3 = 36\pi$.

Flashcard 17: State the formula for the arc length of a circle with radius $r$ and central angle \theta (in radians).

Answer: $s = r\theta$. Arc length equals radius times angle in radians.

Flashcard 18: What is the surface area of a cube with side length $s=4$?

Answer: $SA = 96$. Cube has 6 faces: $6 \times 4^2 = 96$.

Flashcard 19: State the formula for the area of a sector with central angle $\theta$ (degrees) and radius $r$.

Answer: $A = \frac{\theta}{360}\pi r^2$. Fraction of circle's area based on angle ratio.

Flashcard 20: State the formula for the volume of a rectangular prism with dimensions $l,w,h$.

Answer: $V = lwh$. Multiply all three dimensions for box volume.

Flashcard 21: What is the area of a sector with $r=6$ and $\theta=90^\circ$? Express in terms of $\pi$.

Answer: $9\pi$. Sector is $\frac{90}{360} = \frac{1}{4}$ of circle: $\frac{1}{4} \times \pi \times 6^2 = 9\pi$.

Flashcard 22: What is the area of a rectangle with $l=9$ and $w=4$?

Answer: $36$. Apply $A = lw$: $9 \times 4 = 36$.

Flashcard 23: Identify the area of a trapezoid with $b_1=4$, $b_2=10$, and $h=6$.

Answer: $42$. Apply trapezoid formula: $\frac{1}{2}(4+10) \times 6 = 42$.

Flashcard 24: What is the surface area formula for a cylinder with radius $r$ and height $h$?

Answer: $SA=2\pi r^2+2\pi rh$. Two circular bases plus curved lateral surface.

Flashcard 25: Identify the volume of a rectangular prism with $l=4$, $w=3$, and $h=5$.

Answer: $60$. Apply $V = lwh$: $4 \times 3 \times 5 = 60$.

Flashcard 26: What is the volume of a cylinder with $r=2$ and $h=5$ (leave in terms of \pi)?

Answer: $20\pi$. Apply $V=pi r^2h$: $pi imes 2^2 imes 5 = 20pi$.

Flashcard 27: What is the area of a triangle with $b=10$ and $h=6$?

Answer: $30$. Apply $A = \frac{1}{2}bh$: $\frac{1}{2} \times 10 \times 6 = 30$.

Flashcard 28: Identify the volume of a cone with radius $6$ and height $4$.

Answer: $48\pi$. Using $V=\frac{1}{3}\pi r^2h$ with $r=6$ and $h=4$.

Flashcard 29: Identify the scale factor effect: if all lengths scale by $k$, how does volume scale?

Answer: Volume scales by $k^3$. Volume grows with cube of linear scale factor.

Flashcard 30: What is the volume of a cylinder with $r=2$ and $h=5$? Express in terms of $\pi$.

Answer: $20\pi$. Apply $V = \pi r^2h$: $\pi \times 2^2 \times 5 = 20\pi$.

Flashcard 31: Identify the scale factor for area if all linear dimensions are multiplied by $k$.

Answer: Area scales by $k^2$. Area increases by the square of the scale factor.

Flashcard 32: Identify the volume of a cone with $r=6$ and $h=4$ in terms of $\pi$.

Answer: $48\pi$. Apply $V = \frac{1}{3}\pi r^2h$: $\frac{1}{3} \times \pi \times 6^2 \times 4 = 48\pi$.

Flashcard 33: State the formula for the arc length of a circle with radius $r$ and central angle $\theta$ degrees.

Answer: $s = \frac{\theta}{360}\cdot 2\pi r$. Fraction of full circumference based on angle ratio.

Flashcard 34: What is the total surface area of a right circular cylinder with radius $r$ and height $h$?

Answer: $S=2\pi r^2+2\pi rh$. Total surface includes lateral area plus two circular bases.

Flashcard 35: Identify the area of a triangle with $b=10$ and $h=6$.

Answer: $30$. Apply $A=\frac{1}{2}bh=\frac{1}{2}(10)(6)=30$.

Flashcard 36: Identify the scale factor effect: if all lengths scale by $k$, how does area scale?

Answer: Area scales by $k^2$. Area grows with square of linear scale factor.

Flashcard 37: What is the volume of a rectangular prism with $l=5$, $w=3$, and $h=2$?

Answer: $30$. Apply $V = lwh$: $5 \times 3 \times 2 = 30$.

Flashcard 38: State the formula for the area of a sector with central angle \theta (in radians) and radius $r$.

Answer: A = rac{1}{2}r^2\theta. Fraction of circle's area proportional to angle.

Flashcard 39: What is the area of a square with side length $s$?

Answer: $A=s^2$. Square the side length for square area.

Flashcard 40: Find the area of a circle with $r=5$ in terms of $\pi$.

Answer: $25\pi$. Apply $A = \pi r^2 = \pi(5)^2 = 25\pi$.

Flashcard 41: State the formula for the length of an arc with radius $r$ and central angle $\theta$ (degrees).

Answer: $s = \frac{\theta}{360}\cdot 2\pi r$. Arc length is the fraction of circumference based on angle.

Flashcard 42: Identify the area of a trapezoid with bases $8$ and $14$ and height $5$.

Answer: $55$. Using $A=\frac{1}{2}(8+14)(5)=\frac{1}{2}(22)(5)$.

Flashcard 43: What is the volume formula for a prism with base area $B$ and height $h$?

Answer: $V=Bh$. Base area times height for any prism.

Flashcard 44: State the formula for the area of a sector with radius $r$ and central angle $\theta$ (degrees).

Answer: $A = \frac{\theta}{360}\pi r^2$. Fraction of circle's area based on angle ratio.

Flashcard 45: State the formula for the area of a semicircle with radius $r$.

Answer: A = rac{1}{2}\pi r^2. Half a circle's area is $\frac{1}{2}\pi r^2$.

Flashcard 46: State the formula for the surface area of a rectangular prism with dimensions $l,w,h$.

Answer: $SA = 2(lw+lh+wh)$. Sum of all six rectangular face areas.

Flashcard 47: What is the volume formula for a cylinder with radius $r$ and height $h$?

Answer: $V=\pi r^2h$. Circular base area times height.

Flashcard 48: State the formula for the area of a sector with central angle $\theta$ degrees and radius $r$.

Answer: $A = \frac{\theta}{360}\pi r^2$. Sector area is the fraction of circle area based on angle ratio.

Flashcard 49: State the formula for the surface area of a rectangular prism with dimensions $l$, $w$, and $h$.

Answer: $SA = 2(lw+lh+wh)$. Sum of all six rectangular face areas.

Flashcard 50: Identify the area of a rectangle with $l=8$ and $w=3$.

Answer: $24$. Apply $A = lw$: $8 \times 3 = 24$.

Flashcard 51: What is the volume of a cone with $r=3$ and $h=4$? (Leave in terms of $\pi$.)

Answer: $12\pi$. Apply $V = \frac{1}{3}\pi r^2h$: $\frac{1}{3} \times \pi \times 3^2 \times 4 = 12\pi$.

Flashcard 52: State the formula for the area of a sector with radius $r$ and central angle $\theta$ (degrees).

Answer: $A = \frac{\theta}{360}\pi r^2$. Sector area is fraction of circle based on central angle.

Flashcard 53: State the formula for the surface area of a cylinder with radius $r$ and height $h$.

Answer: $SA = 2\pi r^2 + 2\pi rh$. Two circular bases plus curved lateral surface.

Flashcard 54: State the formula for the volume of a rectangular prism with dimensions $l,w,h$.

Answer: $V = lwh$. Product of all three dimensions gives box volume.

Flashcard 55: What is the area of a circle with radius $r=3$?

Answer: $A = 9\pi$. Apply $A = \pi r^2$: $\pi \times 3^2 = 9\pi$.

Flashcard 56: What is the area of a rectangle with $l=8$ and $w=3$?

Answer: $24$. Apply $A=lw$: $8 imes 3 = 24$.

Flashcard 57: State the formula for the volume of a rectangular prism with length $l$, width $w$, and height $h$.

Answer: $V=lwh$. Box volume equals length times width times height.

Flashcard 58: What is the volume formula for a pyramid with base area $B$ and height $h$?

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

Flashcard 59: What is the area of a circle with $r=3$? (Leave in terms of $\pi$.)

Answer: $9\pi$. Apply $A = \pi r^2$: $\pi \times 3^2 = 9\pi$.

Flashcard 60: State the formula for the volume of a sphere with radius $r$.

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

Flashcard 61: State the formula for the volume of a rectangular prism with length $l$, width $w$, height $h$.

Answer: $V = lwh$. Box volume equals length times width times height.

Flashcard 62: State the formula for the surface area of a rectangular prism with dimensions $l,w,h$.

Answer: $SA = 2(lw+lh+wh)$. Sum of all six rectangular face areas.

Flashcard 63: What is the area of a semicircle with radius $r$?

Answer: $A=\frac{1}{2}\pi r^2$. Half of a full circle's area.

Flashcard 64: State the formula for the arc length of a sector with radius $r$ and central angle $\theta$ (degrees).

Answer: $s = \frac{\theta}{360}2\pi r$. Arc length is fraction of circumference based on angle.

Flashcard 65: State the formula for the surface area of a rectangular prism with edges $l$, $w$, and $h$.

Answer: $SA = 2(lw+lh+wh)$. Sum of areas of all six rectangular faces.

Flashcard 66: State the formula for the volume of a right circular cylinder with radius $r$ and height $h$.

Answer: $V=\pi r^2h$. Cylinder volume is base area times height.

Flashcard 67: Find the area of a triangle with base $b=10$ and height $h=7$.

Answer: $35$. Apply $A = \frac{1}{2}bh$: $\frac{1}{2} \times 10 \times 7 = 35$.

Flashcard 68: Identify the area of a circle with diameter $10$.

Answer: $25\pi$. Diameter $10$ gives radius $5$, so area is $\pi(5)^2$.

Flashcard 69: Identify the scale factor for volume if all linear dimensions are multiplied by $k$.

Answer: Volume scales by $k^3$. Volume increases by the cube of the scale factor.

Flashcard 70: State the formula for the volume of a cylinder with radius $r$ and height $h$.

Answer: $V = \pi r^2h$. Base area times height for cylindrical volume.

Flashcard 71: State the formula for the circumference of a circle with radius $r$.

Answer: $C = 2\pi r$. Distance around circle is $2\pi$ times radius.

Flashcard 72: State the formula for the volume of a right circular cone with radius $r$ and height $h$.

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

Flashcard 73: If a rectangle's length doubles and width stays the same, what happens to its area?

Answer: $\text{The area doubles.}$. Since $A = lw$, doubling $l$ doubles the area.

Flashcard 74: State the formula for the area of a sector with radius $r$ and central angle $\theta$ (degrees).

Answer: $A = \frac{\theta}{360}\pi r^2$. Sector area is the fraction of circle area based on angle.

Flashcard 75: What is the volume of a cone with $r=3$ and $h=4$? Express in terms of $\pi$.

Answer: $12\pi$. Apply $V = \frac{1}{3}\pi r^2h$: $\frac{1}{3} \times \pi \times 3^2 \times 4 = 12\pi$.

Flashcard 76: A rectangle's length doubles and width triples; what is the area scale factor?

Answer: $6$. Area scales by product of dimension changes: $2 \times 3 = 6$.

Flashcard 77: State the formula for the volume of a pyramid with base area $B$ and height $h$.

Answer: $V = \frac{1}{3}Bh$. One-third base area times height for any pyramid.

Flashcard 78: A cube has side length $6$. What is its volume?

Answer: $216$. Cube volume is $s^3$: $6^3 = 216$.

Flashcard 79: State the formula for the arc length of a sector with central angle $\theta$ (degrees) and radius $r$.

Answer: $s=\frac{\theta}{360}\cdot 2\pi r$. Fraction of circumference based on angle ratio.

Flashcard 80: What is the area of a triangle with base $b=12$ and height $h=5$?

Answer: $A = 30$. Apply $A = \frac{1}{2}bh$: $\frac{1}{2} \times 12 \times 5 = 30$.

Flashcard 81: State the formula for the area of a trapezoid with bases $b_1,b_2$ and height $h$.

Answer: A = rac{1}{2}(b_1+b_2)h. Average of parallel bases times height.

Flashcard 82: State the formula for the area of a rhombus (or kite) with diagonals $d_1$ and $d_2$.

Answer: A = rac{1}{2}d_1d_2. Half the product of perpendicular diagonals.

Flashcard 83: State the formula for the volume of a right circular cone with radius $r$ and height $h$.

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

Flashcard 84: State the formula for the volume of a rectangular prism with dimensions $l,w,h$.

Answer: $V = lwh$. Box volume equals length times width times height.

Flashcard 85: What is the volume of a cylinder with $r=2$ and $h=7$? (Leave in terms of $\pi$.)

Answer: $28\pi$. Apply $V = \pi r^2h$: $\pi \times 2^2 \times 7 = 28\pi$.

Flashcard 86: State the formula for the area of a circle with radius $r$.

Answer: $A = \pi r^2$. Pi times radius squared gives circular area.

Flashcard 87: State the formula for the volume of a rectangular prism with dimensions $l$, $w$, and $h$.

Answer: $V = lwh$. Product of all three dimensions gives box volume.

Flashcard 88: What is the surface area of a sphere with radius $r$?

Answer: $S=4\pi r^2$. Sphere surface area equals four pi times radius squared.

Flashcard 89: State the formula for the volume of a rectangular prism with dimensions $l,w,h$.

Answer: $V = lwh$. Product of all three dimensions gives box volume.

Flashcard 90: State the formula for the area of a rhombus with diagonals $d_1$ and $d_2$.

Answer: $A = \frac{1}{2}d_1d_2$. Half the product of perpendicular diagonals.

Flashcard 91: Identify the volume of a cylinder with $r=3$ and $h=7$ in terms of $\pi$.

Answer: $63\pi$. Apply $V = \pi r^2h$: $\pi \times 3^2 \times 7 = 63\pi$.

Flashcard 92: If all linear dimensions scale by $k$, what is the volume scale factor?

Answer: $k^3$. Volume scales as cube of linear scale factor.

Flashcard 93: State the formula for the area of a parallelogram with base $b$ and height $h$.

Answer: $A = bh$. Base times perpendicular height for parallelogram area.

Flashcard 94: State the formula for the lateral surface area of a right circular cylinder with radius $r$ and height $h$.

Answer: $\text{LSA} = 2\pi rh$. Lateral area wraps around cylinder: circumference times height.

Flashcard 95: What is the area of a triangle with $b=12$ and $h=5$?

Answer: $30$. Apply $A = \frac{1}{2}bh$: $\frac{1}{2} \times 12 \times 5 = 30$.

Flashcard 96: Identify the area of a triangle with $b=10$ and $h=6$.

Answer: $30$. Apply $A = \frac{1}{2}bh$: $\frac{1}{2} \times 10 \times 6 = 30$.

Flashcard 97: State the formula for the area of a sector with central angle \theta (in degrees) and radius $r$.

Answer: $A=\frac{\theta}{360}\pi r^2$. Fraction of circle's area based on angle ratio.

Flashcard 98: What is the volume of a rectangular prism with $l=5$, $w=2$, and $h=3$?

Answer: $V = 30$. Apply $V = lwh$: $5 \times 2 \times 3 = 30$.

Flashcard 99: State the formula for the area of a rectangle with length $l$ and width $w$.

Answer: $A = lw$. Multiply length by width for rectangular area.

Flashcard 100: Identify the area of a circle with radius $r=5$ in terms of $\pi$.

Answer: $25\pi$. Apply $A = \pi r^2$: $\pi \times 5^2 = 25\pi$.