ACT Math Flashcards: Volume And Surface Area

What this deck covers

This deck focuses on Volume And Surface Area, giving you a quick way to review the definitions, rules, and examples that matter most for ACT 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 volume of a cube with side length $6$?

Answer: $V = 216$. Using $V = s^3$ with $s = 6$.

Flashcard 2: What is the formula for the volume of a cone?

Answer: Volume = $\frac{1}{3}\text{base area} \times \text{height}$. One-third base area times height.

Flashcard 3: Identify the formula for the lateral surface area of a cone.

Answer: $LSA = \pi r l$. Curved surface area excluding the base circle.

Flashcard 4: Find the volume of a rectangular prism with $l=2$, $w=3$, $h=4$.

Answer: $V = 24$. Using $V = l \times w \times h$ with given dimensions.

Flashcard 5: Identify the formula for the lateral surface area of a cone.

Answer: $LSA = \pi r l$. Curved surface area excluding the base circle.

Flashcard 6: What is the volume of a pyramid with base area $B=9$ and height $h=4$?

Answer: $V = 12$. Using $V = \frac{1}{3}Bh$ with given values.

Flashcard 7: Calculate the volume of a cylinder with diameter $10$ and height $7$.

Answer: $V = 175 \pi$. Diameter 10 means radius 5, so $V = \pi(5^2)(7)$.

Flashcard 8: How do you calculate the surface area of a rectangular prism?

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

Flashcard 9: What is the surface area of a cube with side length $7$?

Answer: $SA = 294$. Using $SA = 6s^2$ with $s = 7$.

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

Answer: $SA = \pi r (r + l)$. Base area plus lateral surface area of cone.

Flashcard 11: State the formula for the lateral surface area of a cylinder.

Answer: $LSA = 2 \pi r h$. Curved surface area excluding circular bases.

Flashcard 12: What is the formula for the volume of a cone?

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

Flashcard 13: Find the volume of a rectangular prism with $l=2$, $w=3$, $h=4$.

Answer: Volume = $24$. $2 \times 3 \times 4 = 24$.

Flashcard 14: Find the lateral surface area of a cylinder with radius $4$ and height $10$.

Answer: $LSA = 80 \pi$. Using $LSA = 2\pi rh$ with given values.

Flashcard 15: Calculate the volume of a sphere with radius $3$.

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

Flashcard 16: What is the surface area of a cylinder with $r = 3$ and $h = 4$?

Answer: $SA = 42 \pi$. Using $SA = 2\pi r(r + h)$ with given values.

Flashcard 17: Find the volume of a pyramid with base area $6$ cm$^2$ and height $4$ cm.

Answer: Volume = $8\text{cm}^3$. $\frac{1}{3} \times 6 \times 4 = 8$.

Flashcard 18: What is the lateral surface area of a cone with radius $r=3$ and slant height $l=5$?

Answer: $LSA = 15 \pi$. Using $LSA = \pi rl$ with given values.

Flashcard 19: State the formula for the lateral surface area of a cylinder.

Answer: $LSA = 2 \pi r h$. Curved surface area excluding circular bases.

Flashcard 20: State the formula for the surface area of a sphere.

Answer: $SA = 4 \pi r^2$. Four times the area of a great circle.

Flashcard 21: State the formula for the surface area of a pyramid.

Answer: Surface Area = $\text{base area} + \text{side area}$. Base plus all triangular faces.

Flashcard 22: What is the formula for the volume of a cube?

Answer: Volume = $s^3$, where $s$ is the side length. Cube volume is side cubed.

Flashcard 23: What is the volume of a cylinder with $r = 2$ and $h = 5$?

Answer: $V = 20 \pi$. Using $V = \pi r^2 h$ with given values.

Flashcard 24: Calculate the volume of a cube with side length $8$.

Answer: $V = 512$. Using $V = s^3$ with $s = 8$.

Flashcard 25: Find the surface area of a cube with side length $4$.

Answer: $SA = 96$. Using $SA = 6s^2$ with $s = 4$.

Flashcard 26: Find the surface area of a rectangular prism with $l=3$, $w=4$, $h=5$.

Answer: $SA = 94$. Using $SA = 2(lw + lh + wh)$ with given dimensions.

Flashcard 27: Identify the formula for the volume of a sphere.

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

Flashcard 28: Identify the formula for the volume of a cylinder.

Answer: $V = \pi r^2 h$. Base area times height for circular base shape.

Flashcard 29: State the formula for the surface area of a cube.

Answer: Surface Area = $6s^2$, where $s$ is the side length. Six faces, each area $s^2$.

Flashcard 30: What is the surface area of a cube with side length $7$?

Answer: $SA = 294$. Using $SA = 6s^2$ with $s = 7$.

Flashcard 31: State the formula for the volume of a rectangular prism.

Answer: $V = l \times w \times h$. Multiply length, width, and height to find 3D space.

Flashcard 32: Find the surface area of a sphere with radius $5$.

Answer: $SA = 100 \pi$. Using $SA = 4\pi r^2$ with $r = 5$.

Flashcard 33: What is the volume of a cube with side length $6$?

Answer: $V = 216$. Using $V = s^3$ with $s = 6$.

Flashcard 34: Calculate the volume of a cube with side length $8$.

Answer: $V = 512$. Using $V = s^3$ with $s = 8$.

Flashcard 35: What is the formula for the surface area of a cube?

Answer: $SA = 6s^2$. Six identical square faces, each with area $s^2$.

Flashcard 36: Find the volume of a cone with base radius $r=4$ and height $h=9$.

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

Flashcard 37: What is the formula for the volume of a cube?

Answer: Volume = $s^3$, where $s$ is the side length. Cube volume is side cubed.

Flashcard 38: What is the volume of a pyramid with base area $B=9$ and height $h=4$?

Answer: $V = 12$. Using $V = \frac{1}{3}Bh$ with given values.

Flashcard 39: Calculate the volume of a cylinder with diameter $10$ and height $7$.

Answer: $V = 175 \pi$. Diameter 10 means radius 5, so $V = \pi(5^2)(7)$.

Flashcard 40: State the formula for the volume of a pyramid.

Answer: $V = \frac{1}{3} B h$. One-third of base area times height.

Flashcard 41: State the formula for the surface area of a cube.

Answer: Surface Area = $6s^2$, where $s$ is the side length. Six faces, each area $s^2$.

Flashcard 42: Find the volume of a cube with side $4$ cm.

Answer: Volume = $64 \text{cm}^3$. $4^3 = 64$.

Flashcard 43: What is the formula for the volume of a pyramid?

Answer: Volume = $\frac{1}{3}\text{base area} \times \text{height}$. One-third base area times height.

Flashcard 44: What is the formula for the surface area of a cylinder?

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

Flashcard 45: Identify the volume formula for a triangular prism.

Answer: Volume = $\text{base area} \times \text{height}$. Base area times height.

Flashcard 46: What is the volume of a cylinder with $r = 2$ and $h = 5$?

Answer: $V = 20 \pi$. Using $V = \pi r^2 h$ with given values.

Flashcard 47: What is the formula for the volume of a prism?

Answer: Volume = $\text{base area} \times \text{height}$. Base area times height.

Flashcard 48: What is the formula for the volume of a rectangular prism?

Answer: Volume = $lwh$, where $l$, $w$, and $h$ are dimensions. Length times width times height.

Flashcard 49: Identify the formula for the volume of a sphere.

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

Flashcard 50: Find the surface area of a cube with side length $4$.

Answer: $SA = 96$. Using $SA = 6s^2$ with $s = 4$.

Flashcard 51: State the formula for the volume of a pyramid.

Answer: $V = \frac{1}{3} B h$. One-third of base area times height.

Flashcard 52: State the surface area formula for a prism.

Answer: Surface Area = $2\text{base area} + \text{perimeter} \times \text{height}$. Two bases plus lateral faces.

Flashcard 53: Calculate the surface area of a pyramid with base area $9$ cm$^2$ and side area $12$ cm$^2$.

Answer: Surface Area = $21\text{cm}^2$. $9 + 12 = 21$.

Flashcard 54: Identify the formula for the total surface area of a cone.

Answer: $SA = \pi r (r + l)$. Base area plus lateral surface area of cone.

Flashcard 55: Calculate the volume of a cone with $r = 3$ and $h = 7$.

Answer: $V = 21 \pi$. Using $V = \frac{1}{3}\pi r^2 h$ with given values.

Flashcard 56: Find the volume of a triangular prism with base area $5$ cm$^2$ and height $10$ cm.

Answer: Volume = $50\text{cm}^3$. $5 \times 10 = 50$.

Flashcard 57: How do you calculate the surface area of a rectangular prism?

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

Flashcard 58: Find the volume of a prism with base area $7$ cm$^2$ and height $5$ cm.

Answer: Volume = $35\text{cm}^3$. $7 \times 5 = 35$.

Flashcard 59: State the formula for the surface area of a rectangular prism.

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

Flashcard 60: What is the formula for the volume of a cone?

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

Flashcard 61: Find the surface area of a sphere with radius $5$.

Answer: $SA = 100 \pi$. Using $SA = 4\pi r^2$ with $r = 5$.

Flashcard 62: State the formula for the surface area of a pyramid.

Answer: Surface Area = $\text{base area} + \text{side area}$. Base plus all triangular faces.

Flashcard 63: Calculate the surface area of a cube with side $3$ cm.

Answer: Surface Area = $54 \text{cm}^2$. $6 \times 3^2 = 54$.

Flashcard 64: What is the surface area of a sphere with diameter $10$?

Answer: $SA = 100 \pi$. Diameter 10 means radius 5, so $SA = 4\pi(5^2)$.

Flashcard 65: State the surface area formula for a prism.

Answer: Surface Area = $2\text{base area} + \text{perimeter} \times \text{height}$. Two bases plus lateral faces.

Flashcard 66: Find the volume of a rectangular prism with $l=2$, $w=3$, $h=4$.

Answer: $V = 24$. Using $V = l \times w \times h$ with given dimensions.

Flashcard 67: What is the formula for the surface area of a cylinder?

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

Flashcard 68: State the formula for the volume of a rectangular prism.

Answer: $V = l \times w \times h$. Multiply length, width, and height to find 3D space.

Flashcard 69: What is the surface area of a sphere with diameter $10$?

Answer: $SA = 100 \pi$. Diameter 10 means radius 5, so $SA = 4\pi(5^2)$.

Flashcard 70: Identify the formula for the volume of a cylinder.

Answer: $V = \pi r^2 h$. Base area times height for circular base shape.