Virginia SOL Math / Geometry / Two- & Three-Dimensional Figures
Surface Area & Volume of Solids
What you'll learn
- Find the surface area of prisms, cylinders, and other solids
- Find the volume of prisms, cylinders, cones, and spheres
- Solve real-world problems involving solids
Words to know
- Surface area —
- the total area of all faces of a solid
- Volume —
- the amount of space a solid holds
- Prism —
- a solid with two parallel matching bases
- Cylinder —
- a solid with two circular bases
- Face —
- a flat surface of a solid
Why it matters Surface area tells us how much material wraps a box or tank; volume tells us how much it holds, from shipping to filling a pool.
Worked examples
Model ItI do
Find the volume of this rectangular prism with length 5, width 2, and height 3.
Volume of a prism is length x width x height: V = 5 x 2 x 3 = 30 cubic units.
Try It TogetherWe do
Find the surface area of the same 5 by 2 by 3 rectangular prism.
Add the areas of the three pairs of faces: 2(5x2) + 2(5x3) + 2(2x3) = 2(10) + 2(15) + 2(6) = 20 + 30 + 12 = 62 square units.
Now YouYou do
A cylinder has radius 3 and height 4. Find its volume. Use V = pi x r^2 x h.
Square the radius, multiply by the height and by pi. Check your answer in the back of this chapter.
Practice
Mastered 0 of 11
Warm-up
Ease in with the basics.
1.Find the volume of a rectangular prism 4 by 3 by 2.
2.Find the volume of a cube with edge 3.
3.A prism has base area 10 and height 6. Find its volume.
On Level
The core Quick Check from the book.
1.Find the volume of a prism 4 by 3 by 2.
2.The volume of a cylinder is pi times r^2 times _____.
3.Find the surface area of a cube with edge 2.
4.Find the volume of a cube with edge 3.
5.A prism has base area 10 and height 6. Find its volume.
Challenge
Stretch your thinking.
1.A cylinder has radius 3 and height 4. Find its volume. Use V = pi x r^2 x h.
2.Find the volume of a sphere with radius 3. Use V = (4/3) x pi x r^3.
3.A cone has radius 3 and height 5. Find its volume. Use V = (1/3) x pi x r^2 x h.