3-D Volume - ISEE Middle Level: Mathematics Achievement
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A pyramid has volume $30$, height $5$, and base area $B$ unknown. What is $B$?
A pyramid has volume $30$, height $5$, and base area $B$ unknown. What is $B$?
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$18$. Solve for base area by rearranging the pyramid volume formula.
$18$. Solve for base area by rearranging the pyramid volume formula.
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A cylinder has diameter $10$ and height $4$. What is its volume in terms of $\pi$?
A cylinder has diameter $10$ and height $4$. What is its volume in terms of $\pi$?
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$100\pi$. Use radius half of diameter in $\pi r^2 h$.
$100\pi$. Use radius half of diameter in $\pi r^2 h$.
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What is the volume of a sphere with radius $r = 3$ in terms of $\pi$?
What is the volume of a sphere with radius $r = 3$ in terms of $\pi$?
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$36\pi$. Apply the sphere volume formula with the given radius.
$36\pi$. Apply the sphere volume formula with the given radius.
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What is the volume of a cone with radius $r = 6$ and height $h = 3$ in terms of $\pi$?
What is the volume of a cone with radius $r = 6$ and height $h = 3$ in terms of $\pi$?
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$36\pi$. Calculate one-third of $\pi r^2$ times height.
$36\pi$. Calculate one-third of $\pi r^2$ times height.
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A cone has volume $36\pi$, radius $r = 3$, and height $h$ unknown. What is $h$?
A cone has volume $36\pi$, radius $r = 3$, and height $h$ unknown. What is $h$?
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$12$. Solve for height by rearranging the cone volume formula.
$12$. Solve for height by rearranging the cone volume formula.
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What is the volume of a cylinder with radius $r = 2$ and height $h = 9$ in terms of $\pi$?
What is the volume of a cylinder with radius $r = 2$ and height $h = 9$ in terms of $\pi$?
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$36\pi$. Compute $\pi r^2 h$ with the given values.
$36\pi$. Compute $\pi r^2 h$ with the given values.
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A cone and cylinder share the same base radius $r$ and height $h$. What is $\frac{V_{\text{cone}}}{V_{\text{cyl}}}$?
A cone and cylinder share the same base radius $r$ and height $h$. What is $\frac{V_{\text{cone}}}{V_{\text{cyl}}}$?
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$\frac{1}{3}$. The cone's volume is one-third that of the cylinder with identical base and height.
$\frac{1}{3}$. The cone's volume is one-third that of the cylinder with identical base and height.
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A cylinder has volume $72\pi$ and radius $r = 3$. What is the height $h$?
A cylinder has volume $72\pi$ and radius $r = 3$. What is the height $h$?
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$8$. Solve for height by dividing volume by $\pi r^2$.
$8$. Solve for height by dividing volume by $\pi r^2$.
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What is the volume of a cylinder with radius $r = 3$ and height $h = 5$ in terms of $\pi$?
What is the volume of a cylinder with radius $r = 3$ and height $h = 5$ in terms of $\pi$?
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$45\pi$. Compute the base area $\pi r^2$ and multiply by height.
$45\pi$. Compute the base area $\pi r^2$ and multiply by height.
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What is the volume of a pyramid with base area $B = 27$ and height $h = 6$?
What is the volume of a pyramid with base area $B = 27$ and height $h = 6$?
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$54$. Take one-third of the product of base area and height.
$54$. Take one-third of the product of base area and height.
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What is the volume of a prism with base area $B = 12$ and height $h = 7$?
What is the volume of a prism with base area $B = 12$ and height $h = 7$?
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$84$. Multiply the base area by the height to obtain the volume.
$84$. Multiply the base area by the height to obtain the volume.
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What is the volume of a cube with side length $s = 6$?
What is the volume of a cube with side length $s = 6$?
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$216$. Cube the side length to compute the volume.
$216$. Cube the side length to compute the volume.
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What is the volume of a rectangular prism with $l = 5$, $w = 3$, and $h = 4$?
What is the volume of a rectangular prism with $l = 5$, $w = 3$, and $h = 4$?
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$60$. Multiply the length, width, and height to find the volume.
$60$. Multiply the length, width, and height to find the volume.
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State the formula for the volume of any pyramid in terms of base area $B$ and height $h$.
State the formula for the volume of any pyramid in terms of base area $B$ and height $h$.
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$V = \frac{1}{3}Bh$. The volume is one-third of the base area multiplied by the height to the apex.
$V = \frac{1}{3}Bh$. The volume is one-third of the base area multiplied by the height to the apex.
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State the formula for the volume of any prism in terms of base area $B$ and height $h$.
State the formula for the volume of any prism in terms of base area $B$ and height $h$.
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$V = Bh$. The volume is the base area multiplied by the height, which is the perpendicular distance between bases.
$V = Bh$. The volume is the base area multiplied by the height, which is the perpendicular distance between bases.
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State the formula for the volume of a sphere with radius $r$.
State the formula for the volume of a sphere with radius $r$.
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$V = \frac{4}{3}\pi r^3$. The formula derives from integrating the cross-sectional area of a sphere.
$V = \frac{4}{3}\pi r^3$. The formula derives from integrating the cross-sectional area of a sphere.
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State the formula for the volume of a rectangular prism with length $l$, width $w$, and height $h$.
State the formula for the volume of a rectangular prism with length $l$, width $w$, and height $h$.
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$V = lwh$. The volume is calculated as the product of the three dimensions: length, width, and height.
$V = lwh$. The volume is calculated as the product of the three dimensions: length, width, and height.
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State the formula for the volume of a cube with side length $s$.
State the formula for the volume of a cube with side length $s$.
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$V = s^3$. The volume is the side length raised to the third power, as all dimensions are equal.
$V = s^3$. The volume is the side length raised to the third power, as all dimensions are equal.
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State the formula for the volume of a right rectangular pyramid with base area $B$ and height $h$.
State the formula for the volume of a right rectangular pyramid with base area $B$ and height $h$.
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$V = \frac{1}{3}Bh$. The volume is one-third of the product of the base area and the height perpendicular to the base.
$V = \frac{1}{3}Bh$. The volume is one-third of the product of the base area and the height perpendicular to the base.
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State the formula for the volume of a right circular cone with radius $r$ and height $h$.
State the formula for the volume of a right circular cone with radius $r$ and height $h$.
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$V = \frac{1}{3}\pi r^2 h$. The volume is one-third of the base area $\pi r^2$ multiplied by the height.
$V = \frac{1}{3}\pi r^2 h$. The volume is one-third of the base area $\pi r^2$ multiplied by the height.
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State the formula for the volume of a right circular cylinder with radius $r$ and height $h$.
State the formula for the volume of a right circular cylinder with radius $r$ and height $h$.
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$V = \pi r^2 h$. The volume is the base area $\pi r^2$ multiplied by the height.
$V = \pi r^2 h$. The volume is the base area $\pi r^2$ multiplied by the height.
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A rectangular prism has volume $120$, length $10$, and width $3$. What is the height $h$?
A rectangular prism has volume $120$, length $10$, and width $3$. What is the height $h$?
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$4$. Solve for height by dividing volume by length times width.
$4$. Solve for height by dividing volume by length times width.
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What is the volume of a triangular prism with base area $B = 15$ and prism height $h = 8$?
What is the volume of a triangular prism with base area $B = 15$ and prism height $h = 8$?
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$120$. Multiply the triangular base area by the prism height.
$120$. Multiply the triangular base area by the prism height.
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A sphere has diameter $12$. What is its volume in terms of $\pi$?
A sphere has diameter $12$. What is its volume in terms of $\pi$?
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$288\pi$. Use radius half of diameter in $\frac{4}{3}\pi r^3$.
$288\pi$. Use radius half of diameter in $\frac{4}{3}\pi r^3$.
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A cone has diameter $8$ and height $9$. What is its volume in terms of $\pi$?
A cone has diameter $8$ and height $9$. What is its volume in terms of $\pi$?
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$48\pi$. Use radius half of diameter in $\frac{1}{3}\pi r^2 h$.
$48\pi$. Use radius half of diameter in $\frac{1}{3}\pi r^2 h$.
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