3-D Volume - SSAT Upper Level: Quantitative
Card 1 of 21
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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$V=216$. Cube the side length to compute the volume.
$V=216$. Cube the side length to compute the volume.
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State the volume formula for a right circular cone with radius $r$ and height $h$.
State the volume formula for a right circular cone with radius $r$ and height $h$.
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$V=\frac{1}{3}\pi r^2h$. The volume is one-third the base area, a circle of radius $r$, times the height $h$.
$V=\frac{1}{3}\pi r^2h$. The volume is one-third the base area, a circle of radius $r$, times the height $h$.
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State the volume formula for a pyramid with base area $B$ and height $h$.
State the volume formula for a pyramid with base area $B$ and height $h$.
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$V=\frac{1}{3}Bh$. The volume is one-third the product of the base area and perpendicular height.
$V=\frac{1}{3}Bh$. The volume is one-third the product of the base area and perpendicular height.
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State the volume formula for a prism (any base) with base area $B$ and height $h$.
State the volume formula for a prism (any base) with base area $B$ and height $h$.
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$V=Bh$. The volume is the base area extruded along the height of the prism.
$V=Bh$. The volume is the base area extruded along the height of the prism.
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State the volume formula for a triangular prism with triangle base area $A$ and prism height $h$.
State the volume formula for a triangular prism with triangle base area $A$ and prism height $h$.
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$V=Ah$. The volume is the triangular base area multiplied by the prism's height.
$V=Ah$. The volume is the triangular base area multiplied by the prism's height.
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State the volume formula for a right prism with parallelogram base area $B$ and height $h$.
State the volume formula for a right prism with parallelogram base area $B$ and height $h$.
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$V=Bh$. The volume is the parallelogram base area times the perpendicular height.
$V=Bh$. The volume is the parallelogram base area times the perpendicular height.
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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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$V=60$. Multiply the length, width, and height to find the volume.
$V=60$. Multiply the length, width, and height to find the volume.
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What is the volume of a cylinder with radius $r=3$ and height $h=10$?
What is the volume of a cylinder with radius $r=3$ and height $h=10$?
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$V=90\pi$. Compute the base area as $\pi r^2$ and multiply by height.
$V=90\pi$. Compute the base area as $\pi r^2$ and multiply by height.
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Identify the correct volume if a cube’s side doubles from $s$ to $2s$.
Identify the correct volume if a cube’s side doubles from $s$ to $2s$.
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$V\text{ becomes }8s^3$. Doubling the side length scales the volume by $2^3 = 8$.
$V\text{ becomes }8s^3$. Doubling the side length scales the volume by $2^3 = 8$.
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State the volume formula for a rectangular prism with length $l$, width $w$, and height $h$.
State the volume formula for a rectangular prism with length $l$, width $w$, and height $h$.
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$V=lwh$. The volume is the product of the three perpendicular dimensions of the prism.
$V=lwh$. The volume is the product of the three perpendicular dimensions of the prism.
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What is the volume of a cone with radius $r=6$ and height $h=9$?
What is the volume of a cone with radius $r=6$ and height $h=9$?
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$V=108\pi$. Take one-third of the base area times height for the cone's volume.
$V=108\pi$. Take one-third of the base area times height for the cone's volume.
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What is the volume of a sphere with radius $r=3$?
What is the volume of a sphere with radius $r=3$?
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$V=36\pi$. Apply the sphere volume formula with the given radius.
$V=36\pi$. Apply the sphere volume formula with the given radius.
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What is the volume of a pyramid with base area $B=48$ and height $h=9$?
What is the volume of a pyramid with base area $B=48$ and height $h=9$?
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$V=144$. The volume is one-third the base area multiplied by the height.
$V=144$. The volume is one-third the base area multiplied by the height.
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What is the volume of a prism with base area $B=15$ and height $h=8$?
What is the volume of a prism with base area $B=15$ and height $h=8$?
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$V=120$. Multiply the base area by the height to get the prism volume.
$V=120$. Multiply the base area by the height to get the prism volume.
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What is the volume of a triangular prism with base area $A=12$ and height $h=7$?
What is the volume of a triangular prism with base area $A=12$ and height $h=7$?
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$V=84$. The volume equals the triangular base area times the prism height.
$V=84$. The volume equals the triangular base area times the prism height.
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What is the volume of a cylinder with diameter $10$ and height $4$?
What is the volume of a cylinder with diameter $10$ and height $4$?
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$V=100\pi$. Use radius as half the diameter in the cylinder volume formula.
$V=100\pi$. Use radius as half the diameter in the cylinder volume formula.
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What is the volume of a sphere with diameter $10$?
What is the volume of a sphere with diameter $10$?
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$V=\frac{500}{3}\pi$. Use radius as half the diameter in the sphere volume formula.
$V=\frac{500}{3}\pi$. Use radius as half the diameter in the sphere volume formula.
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State the volume formula for a cube with side length $s$.
State the volume formula for a cube with side length $s$.
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$V=s^3$. The volume equals the side length cubed, as all dimensions are equal.
$V=s^3$. The volume equals the side length cubed, as all dimensions are equal.
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State the volume formula for a right circular cylinder with radius $r$ and height $h$.
State the volume formula for a right circular cylinder with radius $r$ and height $h$.
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$V=\pi r^2h$. The volume is the base area, a circle of radius $r$, multiplied by the height $h$.
$V=\pi r^2h$. The volume is the base area, a circle of radius $r$, multiplied by the height $h$.
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Identify the correct volume scale factor if all linear dimensions triple.
Identify the correct volume scale factor if all linear dimensions triple.
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$\text{Volume factor }=27$. Tripling linear dimensions scales volume by $3^3 = 27$.
$\text{Volume factor }=27$. Tripling linear dimensions scales volume by $3^3 = 27$.
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What is the volume of a composite solid: a $3\times 3\times 8$ prism plus a $3\times 3\times 2$ prism?
What is the volume of a composite solid: a $3\times 3\times 8$ prism plus a $3\times 3\times 2$ prism?
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$V=90$. Add the volumes of the two prisms to find the total composite volume.
$V=90$. Add the volumes of the two prisms to find the total composite volume.
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