8th Grade Math Flashcards: Apply Volume Formulas

What this deck covers

This deck focuses on Apply Volume Formulas, giving you a quick way to review the definitions, rules, and examples that matter most for 8th Grade 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 cone with diameter $8$ and height $9$ in terms of $\pi$?

Answer: $48\pi$. Diameter 8 gives $r=4$; $V=\frac{1}{3}\pi(4^2)(9)=48\pi$.

Flashcard 2: A cylinder has $r=2$. If the height doubles, how does the volume change?

Answer: Volume doubles. Volume $V=\pi r^2h$ is proportional to height.

Flashcard 3: A sphere’s radius is tripled. By what factor does the volume change?

Answer: $27$. Volume scales with $r^3$: if $r$ triples, $V$ increases by $3^3=27$.

Flashcard 4: Find and correct the error: A student wrote cylinder volume as $V=2\pi rh$.

Answer: Correct: $V=\pi r^2h$. Student confused cylinder volume with lateral surface area formula.

Flashcard 5: State the formula for the volume of a cone with radius $r$ and height $h$.

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

Flashcard 6: State the formula for the volume of a cylinder with radius $r$ and height $h$.

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

Flashcard 7: What is the height $h$ of a cone with $V=48\pi$ and $r=6$?

Answer: $4$. Solve $48\pi=\frac{1}{3}\pi(6^2)h$: $48\pi=12\pi h$, so $h=4$.

Flashcard 8: What is the height $h$ of a cylinder with $V=64\pi$ and $r=4$?

Answer: $4$. Solve $64\pi=\pi(4^2)h$ for $h$: $64\pi=16\pi h$, so $h=4$.

Flashcard 9: If a cone and cylinder have the same $r$ and $h$, what fraction of the cylinder's volume is the cone's volume?

Answer: $\frac{1}{3}$. Cone volume formula has factor $\frac{1}{3}$ compared to cylinder.

Flashcard 10: What is the volume of a sphere with diameter $12$ in terms of $\pi$?

Answer: $288\pi$. Diameter 12 gives $r=6$; $V=\frac{4}{3}\pi(6^3)=288\pi$.

Flashcard 11: What is the radius of a sphere with diameter $12$?

Answer: $6$. Radius is half the diameter: $12÷2=6$.

Flashcard 12: What is the volume of a cylinder with diameter $10$ and height $4$ in terms of $\pi$?

Answer: $100\pi$. Diameter 10 gives $r=5$; $V=\pi(5^2)(4)=100\pi$.

Flashcard 13: Identify the missing factor: A cone has volume $V=_\pi r^2h$.

Answer: $\frac{1}{3}$. Cone formula has factor $\frac{1}{3}$ before $\pi r^2h$.

Flashcard 14: What is the volume of a sphere with $r=3$ in terms of $\pi$?

Answer: $36\pi$. Apply $V=\frac{4}{3}\pi r^3$ with $r=3$: $\frac{4}{3}\pi(27)=36\pi$.

Flashcard 15: What is the volume of a cone with $r=3$ and $h=5$ in terms of $\pi$?

Answer: $15\pi$. Apply $V=\frac{1}{3}\pi r^2h$ with $r=3$, $h=5$: $\frac{1}{3}\pi(9)(5)=15\pi$.

Flashcard 16: What is the volume of a cylinder with $r=3$ and $h=5$ in terms of $\pi$?

Answer: $45\pi$. Apply $V=\pi r^2h$ with $r=3$, $h=5$: $\pi(3^2)(5)=45\pi$.

Flashcard 17: State the formula for the volume of a sphere with radius $r$.

Answer: $V=\frac{4}{3}\pi r^3$. Sphere volume uses radius cubed with coefficient $\frac{4}{3}\pi$.

Flashcard 18: What is the radius $r$ of a cylinder with $V=36\pi$ and $h=4$?

Answer: $3$. Solve $36\pi=\pi r^2(4)$ for $r$: $r^2=9$, so $r=3$.

Flashcard 19: What is the radius $r$ of a sphere with $V=\frac{4}{3}\pi(2^3)$?

Answer: $2$. Given expression shows $r^3=8$, so $r=2$.

Flashcard 20: Choose the correct volume formula for a sphere: $\pi r^2h$, $\frac{4}{3}\pi r^3$, or $\frac{1}{3}\pi r^2h$.

Answer: $V=\frac{4}{3}\pi r^3$. Sphere formula has $r^3$, not $r^2h$.

Flashcard 21: Find the volume of a cone with diameter $12$ and height $4$ in terms of $\pi$.

Answer: $48\pi$. Diameter $12$ gives $r=6$, so $V=\frac{1}{3}\pi(6)^2(4)$.

Flashcard 22: Find the volume of a cylinder with diameter $10$ and height $3$ in terms of $\pi$.

Answer: $75\pi$. Diameter $10$ gives $r=5$, so $V=\pi(5)^2(3)$.

Flashcard 23: Find and correct the error: A student wrote the sphere volume as $V=4\pi r^3$.

Answer: Correct: $V=\frac{4}{3}\pi r^3$. Missing the fraction $\frac{1}{3}$ in the coefficient.

Flashcard 24: Which option is the correct volume formula for a cone: $\pi r^2h$ or $\frac{1}{3}\pi r^2h$?

Answer: $V=\frac{1}{3}\pi r^2h$. Cone uses one-third of base times height.

Flashcard 25: Which option is the correct volume formula for a cylinder: $\pi r^2h$ or $\frac{1}{3}\pi r^2h$?

Answer: $V=\pi r^2h$. Cylinder uses full base times height, not one-third.

Flashcard 26: Find the radius $r$ of a sphere with volume $V=\frac{4}{3}\pi\cdot 27$.

Answer: $r=3$. Since $V=36\pi=\frac{4}{3}\pi(27)$, and $27=3^3$, so $r=3$.

Flashcard 27: Find the height $h$ of a cone with volume $V=12\pi$ and radius $r=3$.

Answer: $h=4$. From $12\pi=\frac{1}{3}\pi(3)^2h$, solve $12\pi=3\pi h$ for $h$.

Flashcard 28: Find the height $h$ of a cylinder with volume $V=50\pi$ and radius $r=5$.

Answer: $h=2$. From $50\pi=\pi(5)^2h$, divide by $25\pi$ to get $h=2$.

Flashcard 29: Find the radius $r$ of a cylinder with volume $V=64\pi$ and height $h=16$.

Answer: $r=2$. From $64\pi=\pi r^2(16)$, divide by $16\pi$ to get $r^2=4$.

Flashcard 30: Find the volume of a sphere with $r=3$ in terms of $\pi$.

Answer: $36\pi$. Apply $V=\frac{4}{3}\pi r^3=\frac{4}{3}\pi(3)^3=\frac{4}{3}\pi(27)$.