Volume & Surface Area - ACT Math
Card 1 of 30
Calculate the volume of a cone with $r = 3$ and $h = 7$.
Calculate the volume of a cone with $r = 3$ and $h = 7$.
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$V = 21 \pi$. Using $V = \frac{1}{3}\pi r^2 h$ with given values.
$V = 21 \pi$. Using $V = \frac{1}{3}\pi r^2 h$ with given values.
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Find the surface area of a rectangular prism with $l=3$, $w=4$, $h=5$.
Find the surface area of a rectangular prism with $l=3$, $w=4$, $h=5$.
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$SA = 94$. Using $SA = 2(lw + lh + wh)$ with given dimensions.
$SA = 94$. Using $SA = 2(lw + lh + wh)$ with given dimensions.
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Identify the formula for the lateral surface area of a cone.
Identify the formula for the lateral surface area of a cone.
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$LSA = \pi r l$. Curved surface area excluding the base circle.
$LSA = \pi r l$. Curved surface area excluding the base circle.
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Identify the formula for the volume of a sphere.
Identify the formula for the volume of a sphere.
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$V = \frac{4}{3} \pi r^3$. Four-thirds times pi times radius cubed.
$V = \frac{4}{3} \pi r^3$. Four-thirds times pi times radius cubed.
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State the formula for the volume of a pyramid.
State the formula for the volume of a pyramid.
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$V = \frac{1}{3} B h$. One-third of base area times height.
$V = \frac{1}{3} B h$. One-third of base area times height.
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What is the formula for the volume of a cone?
What is the formula for the volume of a cone?
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$V = \frac{1}{3} \pi r^2 h$. One-third of cylinder volume with same base and height.
$V = \frac{1}{3} \pi r^2 h$. One-third of cylinder volume with same base and height.
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Identify the formula for the total surface area of a cone.
Identify the formula for the total surface area of a cone.
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$SA = \pi r (r + l)$. Base area plus lateral surface area of cone.
$SA = \pi r (r + l)$. Base area plus lateral surface area of cone.
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What is the surface area of a cube with side length $7$?
What is the surface area of a cube with side length $7$?
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$SA = 294$. Using $SA = 6s^2$ with $s = 7$.
$SA = 294$. Using $SA = 6s^2$ with $s = 7$.
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What is the volume of a pyramid with base area $B=9$ and height $h=4$?
What is the volume of a pyramid with base area $B=9$ and height $h=4$?
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$V = 12$. Using $V = \frac{1}{3}Bh$ with given values.
$V = 12$. Using $V = \frac{1}{3}Bh$ with given values.
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Identify the formula for the volume of a cylinder.
Identify the formula for the volume of a cylinder.
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$V = \pi r^2 h$. Base area times height for circular base shape.
$V = \pi r^2 h$. Base area times height for circular base shape.
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What is the formula for the surface area of a cylinder?
What is the formula for the surface area of a cylinder?
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$SA = 2 \pi r (r + h)$. Two circular bases plus lateral surface area.
$SA = 2 \pi r (r + h)$. Two circular bases plus lateral surface area.
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What is the volume of a cube with side length $6$?
What is the volume of a cube with side length $6$?
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$V = 216$. Using $V = s^3$ with $s = 6$.
$V = 216$. Using $V = s^3$ with $s = 6$.
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Find the volume of a rectangular prism with $l=2$, $w=3$, $h=4$.
Find the volume of a rectangular prism with $l=2$, $w=3$, $h=4$.
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$V = 24$. Using $V = l \times w \times h$ with given dimensions.
$V = 24$. Using $V = l \times w \times h$ with given dimensions.
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Find the surface area of a sphere with radius $5$.
Find the surface area of a sphere with radius $5$.
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$SA = 100 \pi$. Using $SA = 4\pi r^2$ with $r = 5$.
$SA = 100 \pi$. Using $SA = 4\pi r^2$ with $r = 5$.
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What is the volume of a cylinder with $r = 2$ and $h = 5$?
What is the volume of a cylinder with $r = 2$ and $h = 5$?
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$V = 20 \pi$. Using $V = \pi r^2 h$ with given values.
$V = 20 \pi$. Using $V = \pi r^2 h$ with given values.
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How do you calculate the surface area of a rectangular prism?
How do you calculate the surface area of a rectangular prism?
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$SA = 2lw + 2lh + 2wh$. Sum of areas of all six rectangular faces.
$SA = 2lw + 2lh + 2wh$. Sum of areas of all six rectangular faces.
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What is the formula for the surface area of a cube?
What is the formula for the surface area of a cube?
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$SA = 6s^2$. Six identical square faces, each with area $s^2$.
$SA = 6s^2$. Six identical square faces, each with area $s^2$.
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Find the volume of a cone with base radius $r=4$ and height $h=9$.
Find the volume of a cone with base radius $r=4$ and height $h=9$.
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$V = 48 \pi$. Using $V = \frac{1}{3}\pi r^2 h$ with given values.
$V = 48 \pi$. Using $V = \frac{1}{3}\pi r^2 h$ with given values.
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Calculate the volume of a cylinder with diameter $10$ and height $7$.
Calculate the volume of a cylinder with diameter $10$ and height $7$.
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$V = 175 \pi$. Diameter 10 means radius 5, so $V = \pi(5^2)(7)$.
$V = 175 \pi$. Diameter 10 means radius 5, so $V = \pi(5^2)(7)$.
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What is the surface area of a cylinder with $r = 3$ and $h = 4$?
What is the surface area of a cylinder with $r = 3$ and $h = 4$?
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$SA = 42 \pi$. Using $SA = 2\pi r(r + h)$ with given values.
$SA = 42 \pi$. Using $SA = 2\pi r(r + h)$ with given values.
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Calculate the volume of a sphere with radius $3$.
Calculate the volume of a sphere with radius $3$.
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$V = 36 \pi$. Using $V = \frac{4}{3}\pi r^3$ with $r = 3$.
$V = 36 \pi$. Using $V = \frac{4}{3}\pi r^3$ with $r = 3$.
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State the formula for the volume of a rectangular prism.
State the formula for the volume of a rectangular prism.
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$V = l \times w \times h$. Multiply length, width, and height to find 3D space.
$V = l \times w \times h$. Multiply length, width, and height to find 3D space.
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Find the surface area of a cube with side length $4$.
Find the surface area of a cube with side length $4$.
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$SA = 96$. Using $SA = 6s^2$ with $s = 4$.
$SA = 96$. Using $SA = 6s^2$ with $s = 4$.
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State the formula for the lateral surface area of a cylinder.
State the formula for the lateral surface area of a cylinder.
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$LSA = 2 \pi r h$. Curved surface area excluding circular bases.
$LSA = 2 \pi r h$. Curved surface area excluding circular bases.
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State the formula for the surface area of a sphere.
State the formula for the surface area of a sphere.
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$SA = 4 \pi r^2$. Four times the area of a great circle.
$SA = 4 \pi r^2$. Four times the area of a great circle.
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What is the lateral surface area of a cone with radius $r=3$ and slant height $l=5$?
What is the lateral surface area of a cone with radius $r=3$ and slant height $l=5$?
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$LSA = 15 \pi$. Using $LSA = \pi rl$ with given values.
$LSA = 15 \pi$. Using $LSA = \pi rl$ with given values.
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What is the surface area of a sphere with diameter $10$?
What is the surface area of a sphere with diameter $10$?
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$SA = 100 \pi$. Diameter 10 means radius 5, so $SA = 4\pi(5^2)$.
$SA = 100 \pi$. Diameter 10 means radius 5, so $SA = 4\pi(5^2)$.
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Calculate the volume of a cube with side length $8$.
Calculate the volume of a cube with side length $8$.
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$V = 512$. Using $V = s^3$ with $s = 8$.
$V = 512$. Using $V = s^3$ with $s = 8$.
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Find the lateral surface area of a cylinder with radius $4$ and height $10$.
Find the lateral surface area of a cylinder with radius $4$ and height $10$.
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$LSA = 80 \pi$. Using $LSA = 2\pi rh$ with given values.
$LSA = 80 \pi$. Using $LSA = 2\pi rh$ with given values.
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State the formula for the surface area of a pyramid.
State the formula for the surface area of a pyramid.
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Surface Area = $\text{base area} + \text{side area}$. Base plus all triangular faces.
Surface Area = $\text{base area} + \text{side area}$. Base plus all triangular faces.
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