ISEE Upper Level Mathematics Achievement Flashcards: 3 D Volume

What this deck covers

This deck focuses on 3 D Volume, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Upper Level Mathematics Achievement.

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 cylinder with diameter $d=10$ and height $h=3$ in terms of $\pi$?

Answer: $75\pi$. Uses radius as half the diameter in the cylinder volume formula.

Flashcard 2: State the formula for the volume of a pyramid with base area $B$ and height $h$.

Answer: $V = \frac{1}{3}Bh$. Takes one-third of the product of base area and height for the pyramid's volume.

Flashcard 3: State the formula for the volume of a sphere with radius $r$.

Answer: $V = \frac{4}{3}\pi r^3$. Integrates the cross-sectional areas to derive the volume enclosed by the sphere.

Flashcard 4: State the formula for the volume of a cylinder with radius $r$ and height $h$.

Answer: $V = \pi r^2 h$. Multiplies the circular base area by the height to determine the cylinder's volume.

Flashcard 5: What is the volume of a cube with side length $s=4$?

Answer: $64$. Cubes the side length to find the volume of the cube.

Flashcard 6: What is the volume of a pyramid with base area $B=30$ and height $h=9$?

Answer: $90$. Divides the product of base area and height by three for the pyramid's volume.

Flashcard 7: State the formula for the volume of a cone with radius $r$ and height $h$.

Answer: $V = \frac{1}{3}\pi r^2 h$. Uses one-third of the cylinder volume formula due to the tapering shape of the cone.

Flashcard 8: State the formula for the volume of a cylinder using diameter $d$ and height $h$.

Answer: $V = \frac{1}{4}\pi d^2 h$. Substitutes radius as half the diameter into the standard cylinder volume formula.

Flashcard 9: Identify the volume of a square pyramid with base side $s=6$ and height $h=5$.

Answer: $60$. Calculates one-third of the square base area times height for the pyramid.

Flashcard 10: What is the height $h$ of a cylinder with volume $V=100\pi$ and radius $r=5$?

Answer: $4$. Solves for height by dividing volume by $\pi r^2$ in the cylinder formula.

Flashcard 11: State the formula for the volume of a hemisphere with radius $r$.

Answer: $V = \frac{2}{3}\pi r^3$. Represents half the volume of a full sphere with the same radius.

Flashcard 12: What is the radius $r$ of a sphere with volume $V=\frac{4}{3}\pi(2^3)$?

Answer: $2$. Identifies the radius from the given volume expression matching the sphere formula.

Flashcard 13: What is the volume of a sphere with radius $r=3$ in terms of $\pi$?

Answer: $36\pi$. Applies the sphere volume formula with the given radius cubed.

Flashcard 14: State the formula for the volume of a rectangular prism with length $l$, width $w$, and height $h$.

Answer: $V = lwh$. Multiplies the three dimensions to determine the enclosed space in a rectangular prism.

Flashcard 15: What is the volume of a cone with $r=3$ and $h=4$ in terms of $\pi$?

Answer: $12\pi$. Takes one-third of $\pi r^2 h$ to calculate the cone's volume.

Flashcard 16: State the formula for the volume of a triangular prism with base area $B$ and prism height $h$.

Answer: $V = Bh$. Multiplies the triangular base area by the prism height to find the total volume.

Flashcard 17: What is the volume of a hemisphere with radius $r=6$ in terms of $\pi$?

Answer: $144\pi$. Uses half of the full sphere's volume for the hemisphere with the given radius.

Flashcard 18: State the formula for the volume of a square pyramid with base side $s$ and height $h$.

Answer: $V = \frac{1}{3}s^2h$. Applies one-third of the base area times height for a pyramid with square base.

Flashcard 19: What is the volume of a rectangular prism with $l=6$, $w=2$, and $h=5$?

Answer: $60$. Multiplies length, width, and height to compute the rectangular prism's volume.

Flashcard 20: State the formula for the volume of a right circular cone using diameter $d$ and height $h$.

Answer: $V = \frac{1}{12}\pi d^2 h$. Substitutes radius as half the diameter into the standard cone volume formula.

Flashcard 21: State the formula for the volume of any prism with base area $B$ and height $h$.

Answer: $V = Bh$. Multiplies the base area by the height to calculate the volume for any prism.

Flashcard 22: What is the volume of a cone with diameter $d=12$ and height $h=8$ in terms of $\pi$?

Answer: $96\pi$. Substitutes radius as half the diameter into the cone volume formula.

Flashcard 23: What is the volume of a prism with base area $B=18$ and height $h=7$?

Answer: $126$. Multiplies the base area by the height to find the prism's volume.

Flashcard 24: State the formula for the volume of a cube with side length $s$.

Answer: $V = s^3$. Cubes the side length since all dimensions are equal in a cube.

Flashcard 25: What is the volume of a cylinder with $r=3$ and $h=5$ in terms of $\pi$?

Answer: $45\pi$. Multiplies the base area $\pi r^2$ by height to obtain the cylinder's volume.