Area & Volume - PSAT Math
Card 1 of 30
State the formula for the volume of a cone with radius $r$ and height $h$.
State the formula for the volume of a cone with radius $r$ and height $h$.
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$V = \frac{1}{3}\pi r^2h$. One-third of cylinder volume with same base and height.
$V = \frac{1}{3}\pi r^2h$. One-third of cylinder volume with same base and height.
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State the formula for the volume of a cylinder with radius $r$ and height $h$.
State the formula for the volume of a cylinder with radius $r$ and height $h$.
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$V = \pi r^2h$. Base area times height for cylindrical volume.
$V = \pi r^2h$. Base area times height for cylindrical volume.
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State the formula for the volume of a rectangular prism with dimensions $l$, $w$, and $h$.
State the formula for the volume of a rectangular prism with dimensions $l$, $w$, and $h$.
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$V = lwh$. Product of all three dimensions gives box volume.
$V = lwh$. Product of all three dimensions gives box volume.
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State the formula for the area of a rhombus with diagonals $d_1$ and $d_2$.
State the formula for the area of a rhombus with diagonals $d_1$ and $d_2$.
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$A = \frac{1}{2}d_1d_2$. Half the product of perpendicular diagonals.
$A = \frac{1}{2}d_1d_2$. Half the product of perpendicular diagonals.
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State the formula for the arc length of a sector with central angle $\theta$ (degrees) and radius $r$.
State the formula for the arc length of a sector with central angle $\theta$ (degrees) and radius $r$.
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$s = \frac{\theta}{360}\cdot 2\pi r$. Fraction of circumference based on angle ratio.
$s = \frac{\theta}{360}\cdot 2\pi r$. Fraction of circumference based on angle ratio.
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State the formula for the area of a sector with central angle $\theta$ (degrees) and radius $r$.
State the formula for the area of a sector with central angle $\theta$ (degrees) and radius $r$.
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$A = \frac{\theta}{360}\pi r^2$. Fraction of circle's area based on angle ratio.
$A = \frac{\theta}{360}\pi r^2$. Fraction of circle's area based on angle ratio.
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State the formula for the circumference of a circle with radius $r$.
State the formula for the circumference of a circle with radius $r$.
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$C = 2\pi r$. Distance around circle is $2\pi$ times radius.
$C = 2\pi r$. Distance around circle is $2\pi$ times radius.
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State the formula for the area of a circle with radius $r$.
State the formula for the area of a circle with radius $r$.
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$A = \pi r^2$. Pi times radius squared gives circular area.
$A = \pi r^2$. Pi times radius squared gives circular area.
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State the formula for the area of a trapezoid with bases $b_1,b_2$ and height $h$.
State the formula for the area of a trapezoid with bases $b_1,b_2$ and height $h$.
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$A = rac{1}{2}(b_1+b_2)h$. Average of parallel bases times height.
$A = rac{1}{2}(b_1+b_2)h$. Average of parallel bases times height.
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Find the area of a rectangle with $l=9$ and $w=4$.
Find the area of a rectangle with $l=9$ and $w=4$.
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$36$. Apply $A = lw$: $9 \times 4 = 36$.
$36$. Apply $A = lw$: $9 \times 4 = 36$.
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State the formula for the area of a parallelogram with base $b$ and height $h$.
State the formula for the area of a parallelogram with base $b$ and height $h$.
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$A = bh$. Base times perpendicular height for parallelogram area.
$A = bh$. Base times perpendicular height for parallelogram area.
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State the formula for the area of a triangle with base $b$ and height $h$.
State the formula for the area of a triangle with base $b$ and height $h$.
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$A = rac{1}{2}bh$. Half the product of base and height gives triangular area.
$A = rac{1}{2}bh$. Half the product of base and height gives triangular area.
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State the formula for the arc length of a circle with radius $r$ and central angle $ \theta$ (in radians).
State the formula for the arc length of a circle with radius $r$ and central angle $ \theta$ (in radians).
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$s = r\theta$. Arc length equals radius times angle in radians.
$s = r\theta$. Arc length equals radius times angle in radians.
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State the formula for the area of a trapezoid with bases $b_1, b_2$ and height $h$.
State the formula for the area of a trapezoid with bases $b_1, b_2$ and height $h$.
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$A = rac{1}{2}(b_1+b_2)h$. Average of parallel bases times height.
$A = rac{1}{2}(b_1+b_2)h$. Average of parallel bases times height.
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Find the area of a triangle with $b=10$ and $h=6$.
Find the area of a triangle with $b=10$ and $h=6$.
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$30$. Apply $A = \frac{1}{2}bh$: $\frac{1}{2} \times 10 \times 6 = 30$.
$30$. Apply $A = \frac{1}{2}bh$: $\frac{1}{2} \times 10 \times 6 = 30$.
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Find the area of a rectangle with $l=8$ and $w=3$.
Find the area of a rectangle with $l=8$ and $w=3$.
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$24$. Apply $A = lw$: $8 \times 3 = 24$.
$24$. Apply $A = lw$: $8 \times 3 = 24$.
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State the formula for the area of a rhombus (or kite) with diagonals $d_1$ and $d_2$.
State the formula for the area of a rhombus (or kite) with diagonals $d_1$ and $d_2$.
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$A = rac{1}{2}d_1d_2$. Half the product of perpendicular diagonals.
$A = rac{1}{2}d_1d_2$. Half the product of perpendicular diagonals.
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State the formula for the arc length of a circle with radius $r$ and central angle $\theta$ degrees.
State the formula for the arc length of a circle with radius $r$ and central angle $\theta$ degrees.
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$s = \frac{\theta}{360}\cdot 2\pi r$. Fraction of full circumference based on angle ratio.
$s = \frac{\theta}{360}\cdot 2\pi r$. Fraction of full circumference based on angle ratio.
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State the formula for the area of a sector with radius $r$ and central angle $\theta$ degrees.
State the formula for the area of a sector with radius $r$ and central angle $\theta$ degrees.
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$A = \frac{\theta}{360}\pi r^2$. Fraction of full circle area based on angle ratio.
$A = \frac{\theta}{360}\pi r^2$. Fraction of full circle area based on angle ratio.
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State the formula for the surface area of a rectangular prism with dimensions $l,w,h$.
State the formula for the surface area of a rectangular prism with dimensions $l,w,h$.
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$SA = 2(lw+lh+wh)$. Sum of all six face areas, paired opposites.
$SA = 2(lw+lh+wh)$. Sum of all six face areas, paired opposites.
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State the formula for the volume of a rectangular prism with dimensions $l,w,h$.
State the formula for the volume of a rectangular prism with dimensions $l,w,h$.
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$V = lwh$. Product of all three dimensions gives box volume.
$V = lwh$. Product of all three dimensions gives box volume.
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What is the volume of a cylinder with $r=2$ and $h=10$? (Leave in terms of $\pi$.)
What is the volume of a cylinder with $r=2$ and $h=10$? (Leave in terms of $\pi$.)
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$40\pi$. Apply $V = \pi r^2h$: $\pi \times 2^2 \times 10 = 40\pi$.
$40\pi$. Apply $V = \pi r^2h$: $\pi \times 2^2 \times 10 = 40\pi$.
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What is the area of a circle with $r=3$? (Leave in terms of $\pi$.)
What is the area of a circle with $r=3$? (Leave in terms of $\pi$.)
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$9\pi$. Apply $A = \pi r^2$: $\pi \times 3^2 = 9\pi$.
$9\pi$. Apply $A = \pi r^2$: $\pi \times 3^2 = 9\pi$.
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What is the area of a triangle with $b=12$ and $h=5$?
What is the area of a triangle with $b=12$ and $h=5$?
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$30$. Apply $A = \frac{1}{2}bh$: $\frac{1}{2} \times 12 \times 5 = 30$.
$30$. Apply $A = \frac{1}{2}bh$: $\frac{1}{2} \times 12 \times 5 = 30$.
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What is the area of a rectangle with $l=9$ and $w=4$?
What is the area of a rectangle with $l=9$ and $w=4$?
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$36$. Apply $A = lw$: $9 \times 4 = 36$.
$36$. Apply $A = lw$: $9 \times 4 = 36$.
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State the formula for the area of a rectangle with length $l$ and width $w$.
State the formula for the area of a rectangle with length $l$ and width $w$.
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$A = lw$. Multiply length by width for rectangular area.
$A = lw$. Multiply length by width for rectangular area.
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State the formula for the volume of a pyramid with base area $B$ and height $h$.
State the formula for the volume of a pyramid with base area $B$ and height $h$.
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$V = \frac{1}{3}Bh$. One-third base area times height for any pyramid.
$V = \frac{1}{3}Bh$. One-third base area times height for any pyramid.
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State the formula for the surface area of a cylinder with radius $r$ and height $h$.
State the formula for the surface area of a cylinder with radius $r$ and height $h$.
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$SA = 2\pi r^2 + 2\pi rh$. Two circular bases plus curved lateral surface.
$SA = 2\pi r^2 + 2\pi rh$. Two circular bases plus curved lateral surface.
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State the formula for the surface area of a rectangular prism with dimensions $l$, $w$, and $h$.
State the formula for the surface area of a rectangular prism with dimensions $l$, $w$, and $h$.
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$SA = 2(lw+lh+wh)$. Sum of all six rectangular face areas.
$SA = 2(lw+lh+wh)$. Sum of all six rectangular face areas.
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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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$V = \frac{4}{3}\pi r^3$. Four-thirds pi times radius cubed for spherical volume.
$V = \frac{4}{3}\pi r^3$. Four-thirds pi times radius cubed for spherical volume.
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