MG2
Name_____________________
William H. Maxwell CTE
Mr. Badette, Principal
Department of Mathematics
Andrew Uwa, Assistant Principal
Volume/ Surface Area of Solids Project
Common Core Standards:
G-GMD.1. Give an informal argument for the formulas for the circumference of a circle, area of a circle,
volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal
limit arguments.
G-GMD.2. Give an informal argument using Cavalieri’s principle for the formulas for the volume of a
sphere and other solid figures.
G-GMD.3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems
G-MG.3. Apply geometric methods to solve design problems (e.g., designing an object or structure to
satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
Lesson 21
G.G. 14c
Common Core
Standards:
G-MG.1, 2
Lesson 22
Aim: What is solid geometry?
Common Core
Standards:
7.G.6
Lesson 23,24
G.G. 10, 11, 14b
Common Core
Standards:
G-MG.1, 2
McDougal Littell: pp# 720 - 736
Lesson 25,26
G.G. 14
Common Core
Standards:
G-MG.1, 2
Aim: What are the properties of a Cylinder and How do we find the volume
and surface area of cylinders?
Lesson 27,28
G.G. 15
Common Core
Standards:
G-MG.1, 2
Aim: What are the properties of a Cone and How do we find the volume and
surface area of right circular cones?
McDougal Littell: pp# 790 - 801
(include Polyhedron and Platonic solids, classification, nets)
Aim: How do we find areas of polygons and circles?
(include triangles, parallelograms(all) , trapezoids, circles)
Aim: What are the properties of a Prism and How do we find the volume and
surface area of prisms?
McDougal Littell: pp# 803-809,819 – 825
(include lateral area)
McDougal Littell: pp# 803-809,819 – 825
(include lateral area)
McDougal Littell: pp# 812 -815, 829 -836
(include lateral area)
Lesson 29
G.G. 13
Common Core
Standards:
G-MG.1, 2
Aim: What are the properties of Pyramids and How do we find the volume and
surface area of Pyramids?
Lesson 30
G.G. 16
Common Core
Standards:
G-MG.1, 2
Lesson 31
G.G. 16
Common Core
Standards:
G-MG.1, 2
Aim: What are the properties of a sphere and How do we find the volume and
surface area of spheres?
McDougal Littell: pp# 812 -815, 829 -836
(include lateral area)
McDougal Littell: pp# 838 -845
Aim: What is a relationship between perimeters, areas and volumes of similar
shapes?
McDougal Littell: pp# 737 -745
In your group (3 students per group)
1. Write three different sets of dimensions that you could use to build a rectangular prism that has a
volume of your choice. (Each group must have a unique number)
a. Length : _______
Width: _______
Height: _______
b. Length : _______
Width: _______
Height: ________
c. Length : ________
Width: ________
Height: ________
Assign each set of dimensions to a different group member.
On your own:
2. Create a 3-dimensional sketch of your assigned rectangular prism below.
Label the length, the width, and the height.
Suppose your assigned rectangular prism is a fish tank, which has only 5 faces and an
open top.
There are three ways to turn your fish tank.
You can turn it so;
 the height is perpendicular to your desk,
 the length is perpendicular to your desk,
 the width is perpendicular to your desk.
You may want to label the length, width, and height on your model to help you with the following questions.
3. With the height perpendicular to your desk, find the surface area of the fish tank.
Explain your answer. (Remember: The top is always the missing face of your fish tank, so when you turn it,
a different face is missing.)
4. Turn your rectangular prism so the length is perpendicular to the desk. What is the surface area? Did it
change? Explain your answer.
5. Turn your rectangular prism so that the width is perpendicular to the desk. What is the surface area? Did
it change? Explain your answer.
The Tropical Fish Company has hired you to build a glass fish tank that is both visually appealing and
cheap to construct.
8. Glass costs $0.15 per square foot. Find the cost of the glass for each of the 3 possible fish tank
configurations.
9. What is the best fish tank design? Write a convincing proposal to the fish tank company on which design to
use and why.
(Answer to this question must be written or typed on a separate piece of paper)
In your group: Share your answers.
After all group members have shared their answers, answer the questions below.
10. Compare the volumes of the three rectangular prisms. What do you notice?
11. Compare the surface areas of the 3 rectangular prisms. What were the largest and smallest surface areas?
What were the dimensions of the prisms with these surface areas?
On your own:
12. Compare your fish tank proposal from Question 9 with other student’s proposals. Revise your proposal to
explain why your design is better than others.
(Answer to this question must be written or typed on a separate piece of paper)
13. Which fish tank proposal do you think the company should accept? Why?