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Study Guides > ALGEBRA / TRIG I

Summary: Solving Problems Using Volume and Surface Area

Key Concepts

  • Volume and Surface Area of a Rectangular Solid
    • [latex]V=LWH[/latex]
    • [latex]S=2LH+2LW+2WH[/latex]
  • Volume and Surface Area of a Cube
    • [latex]V={s}^{3}[/latex]
    • [latex]S=6{s}^{2}[/latex]
  • Volume and Surface Area of a Sphere
    • [latex]V=\Large\frac{4}{3}\normalsize\pi {r}^{3}[/latex]
    • [latex]S=4\pi {r}^{2}[/latex]
  • Volume and Surface Area of a Cylinder
    • [latex]V=\pi {r}^{2}h[/latex]
    • [latex]S=2\pi {r}^{2}+2\pi rh[/latex]
  • Volume of a Cone
    • For a cone with radius [latex]r[/latex] and height [latex]h[/latex] :Volume: [latex]V=\Large\frac{1}{3}\normalsize\pi {r}^{2}h[/latex]

Glossary

cone
A cone is a solid figure with one circular base and a vertex.
cube
A cube is a rectangular solid whose length, width, and height are equal.
cylinder
A cylinder is a solid figure with two parallel circles of the same size at the top and bottom.
 

Summary of Geometry Formulas

The following charts summarize all of the formulas covered in this chapter. A table is shown that summarizes all of the formulas in the chapter. The first cell is for Supplementary and Complementary Angles, and says that the measure of angle A plus the measure of angle B equals 180 degrees for supplementary angles A and B and the measure of angle C plus the measure of angle D equals 90 degrees for complementary angles C and D. There is an image of two angles A and B that together form a straight line and two angles C and D that together form a right angle. The next cell says Rectangular Solid and shows the formulas Volume equals LWH and Surface Area equals 2LH plus 2LW plus 2WH. An image of a rectangular solid with sides L, W, and H is shown. The next cell says Triangle. An image of a triangle is shown with sides a, b, and c, vertices A, B, and C, and height h. It says, This image shows a row with three columns. The first column says Rectangular solid with the formula below that says volume: V equals LWH. Under this, it says Surface Area: S equals 2LH plus 2LW plus 2WH. An image shows an image of a rectangular solid with the sides labeled L , W and H. The middle column says Rectangle. Under this it says Perimeter P equals 2L plus 2W, then Area A equals LW. An image of a rectangle with sides W and L. The right column says Cube. Under this it says

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