Name _______________________________________________ Date:_____________________ Per:_______
Filling and Wrapping
F&W Unit Review CC7/8
Show all work to support your answers. No work, No credit! Use 3.14 for pi.
Use the following information to answer Exercises 1–3.
A movie theater sells two sizes of popcorn. One box has the shape of the triangular prism (Popcorn T). The
other box has the shape of a rectangular prism (Popcorn R). The boxes do not have tops!
Popcorn T
Popcorn R
8.7 cm
15 cm
Equilateral triangle
10 cm.
1 a. How many square cm of cardboard are needed to make each box? Show your work.
Work for Popcorn T
Work for Popcorn R
b. Which box needs more cardboard? _______________________________________
2a. How many cubic cm of popcorn will fit in each box if the top of the popcorn is level with the top
of the box? Show your work.
Work for Popcorn T
Work for Popcorn R
b. Which box holds more?________________________________________________
3. Suppose the theater decides to sell a third popcorn size, the family-size box. The family-size box
is a rectangular prism without a top. The scale factor from the rectangular box (Popcorn R) to
the family-size box is 2.
a. What is the surface area of the family-size box?
b. What is the volume of the family-size box?
c. Suppose the Popcorn R box sells for $1.75. What should be the price of the family-size box if
it is based on the amount of popcorn the box holds?
4. One face of a cube has an area of 81 cm².
a. What is the surface area of the cube? Show your work.
b. What is the volume of the cube?
5. a. Name the two solid figures that will result from a cut in the direction shown.
1)______________________________
2)______________________________
b. Name the two-dimensional shape of the face formed by the cut. __________________
6.
Find the surface area and volume of the regular pentagonal prism shown below.
The base has an area of 43.7 square centimeters.
Surface Area :
Volume:
7cm
Mixed Review
7. Find the slope and y-intercept of the
equation y = -x – 8
8. Find the slope of the line below. Use
the points given. Show your work.
Slope = ________
y-int. = ________
Solve each equation below. Show all steps.
9. 5(6x – 8) = 5x + 10
10. 8 – 4(6x – 2) = 24
11. 6(7x + 8) = -120
12.
A pizzeria sells a round pizza with diameter 18 inches. Another pizzeria sells a large square pizza with side
length 16 inches.
a. Which of the two shapes gives you more pizza? Show your work.
Work for the round pizza
Work for the square pizza
Which shape gives you more pizza and how much more?
b. Which has more crust along the outside edge of the pizza, the square pizza or the round pizza?
Show how you found your answer.
Work for the round pizza
Work for the square pizza
Which shape gives you more pizza crust and how much more?
4cm
13. At the right are scale drawings of two
cylinders. One cylinder has a diameter of 4 cm
and a height of 12 cm. The other cylinder has a
diameter of 12 cm and a height of 4 cm.
12cm
a. Do the cylinders have the same volume?
Show your work.
12cm
4cm
14. Find the volume of the cone. Show your work.
9 in.
4 in.