MK · 8 cards

Area, Surface Area and Volume flashcards

8 cards with the formulas, rules and traps from this lesson. Answer in your head, then flip to check.

Formula · 1/8
Trapezoid area: what is the formula?
$A = \frac{1}{2} (b_{1} + b_{2}) h$ : average the two parallel bases $b_{1}, b_{2}$ and multiply by the perpendicular height h. Bases 5 and 9 with height 6 give 42 square units.
Formula · 2/8
Volume of any prism or cylinder?
$V = B h$ , where B is the area of one base and h is the distance between the bases. For a cylinder $B = π r^{2}$ , so $V = π r^{2} h$ . Answer in cubic units.
Rule · 3/8
How does the volume of a pyramid or cone compare with a prism or cylinder of the same base and height?
It is one third: $V = \frac{1}{3} B h$ for a pyramid and $V = \frac{1}{3} π r^{2} h$ for a cone. Pointed solids carry the one-third.
Formula · 4/8
Volume and surface area of a sphere of radius r?
$V = \frac{4}{3} π r^{3}$ (cubic units) and $S A = 4 π r^{2}$ (square units). For r = 6, $V = 288 π$ .
Formula · 5/8
Total surface area of a closed cylinder?
$S A = 2 π r^{2} + 2 π r h$ : two circular ends plus the curved side (a rectangle whose width is the circumference $2 π r$ ). Open top: drop one $π r^{2}$ .
Common trap · 6/8
Cone or pyramid: when do you use the slant height l and when the vertical height h?
Volume uses the vertical height h; surface area uses the slant height l. They are linked by a right triangle, e.g. for a cone $l^{2} = r^{2} + h^{2}$ .
Rule · 7/8
If every length of a figure is multiplied by k, what happens to area and volume?
Area (and surface area) is multiplied by $k^{2}$ ; volume by $k^{3}$ . Doubling all dimensions gives 4 times the surface and 8 times the volume.
Fact · 8/8
Key square and cubic unit conversions for feet, inches and yards?
Square the length factor for area and cube it for volume: $1 ft^{2} = 144 in^{2}$ , $1 ft^{3} = 1728 in^{3}$ , $1 yd^{3} = 27 ft^{3}$ . Also 1 liter = 1000 cubic centimeters.

← Circles Coordinate Geometry and Graphs →