1. Volume and Surface Area
Chapter 10
Volume and Surface Area

2. (Not in the book.)
A Review of Area

3. Area Formulas
Triangle
Parallelogram
Trapezoid
Square
Rectangle

4. Area Challenge With your group, complete Sheet 1 together.
You may use the Formula Cards provided to assist you.
When you are finished with that side, you must have it checked for accuracy before moving on to Sheet 2.
With your group, complete Sheet 2.
When you are finished with Sheet 2, raise your hand to let your teacher know your table is ready.
If Sheet 2 is correct, you will receive Sheet 3 – applying this skill to a real life situation.
With your group, complete Sheet 3. Raise your hand to have your paper checked.
THERE WILL BE A SMALL TREAT FOR THOSE GROUPS WHO CAN ALL FINISH SHEET THREE CORRECTLY BEFORE CLASS IS OVER.

5. Prisms and Pyramids
Volume

6. Volume of Prisms
A prism is a three-dimensional figure with at least three rectangular lateral faces and top and bottom faces that are parallel.
The volume of a three-dimensional figure is the measure of space it occupies.
It is measured in CUBIC UNITS.
A rectangular prism is a prism that has rectangular bases.

7. Rectangular Prism Practice
Find the volume of each prism.
A concession stand serves peanuts in two different containers. Which container holds more peanuts? Justify your answer.
142.5 m3
24 cm3
Box B holds more peanuts.
Box A: in3
Box B: 73 in3

8. Triangular Prism Practice
Volume of Prisms
A triangular prism is a prism that has triangular bases.
Triangular Prism Practice
70 in3
46.8 mm3

9. Volume of Pyramids
A pyramid is a three-dimensional figure with one base and triangular lateral faces, or any flat surfaces that are not bases.

10. Pyramid Practice
Find the volume of the pyramid. Round to the nearest tenth.
9.7 in3
A triangular pyramid has a volume of 60 cubic centimeters. The triangular base has a 12-centimeter base and a 5-centimeter height. Find the height of the pyramid.
6 cm
A scale model of the Egyptian pyramid is shown. Find the volume of the square pyramid.
216 in3

11. Prisms and Pyramids
Surface Area

12. Surface Area of Prisms EXAMPLE
The sum of the areas of all the surfaces, or faces, of a three-dimensional figure is the surface area.
HOW DO WE DO THAT?
Find the AREA of each FACE.
ADD all the AREAS together.
You may need to look back in your notes for area formulas.
EXAMPLE
Find the surface area of the rectangular prism.
top and bottom: 2(5×4) = 40
front and back: 2(5×3) = 30
two sides: 2(3×4) = 24
Sum of the ALL the AREAS: 94 square centimeters

13. Prism Practice Find the surface area of each prism.
If one gallon of paint covers 350 square feet, will 8 gallons of paint be enough to paint the inside and outside of the fence shown? EXPLAIN.
216 m2
864 mm2
mm2
195 in2
Yes.
2520 ft2 < 2800 ft2

14. Surface Are of Pyramids
A right square pyramid has a square base and four isosceles triangles that make up the lateral faces.
The height of each lateral face is called the slant height (𝓁).
The lateral surface area (L) of a solid is the sum of the areas of all its lateral faces.
Total Surface Area of a Regular Pyramid:
𝑆.𝐴.=𝐵+ 1 2 𝑃𝓁

15. Pyramid Examples

16. Pyramid Practice
Find the total surface area of the pyramid. Round to the nearest tenth.
41 in2
Find the total surface area of the pyramid with a base area of square centimeters.
484.1 cm2
A game piece for a board game is shaped like a square pyramid. It has a slant height of 15 millimeters and the bases have edges 11 millimeters long. What is the surface area of the game piece?
451 mm2