IM 1
Investigation 5.3.3
Name
Show calculations for all problems and round to the nearest hundredth.
1) A large box made of cardboard is used to ship a refrigerator so the volume needs to be 50.96 cubic feet.
The box is in the shape of a square prism with a height of 6.5 feet. The formula for the volume of the box
is V  L2  H where L = side length of the square, and H = height of the box.
a) What is the side length of the box? Solve algebraically.
b) What is the total surface area of the cardboard box?
c) If the cost of the cardboard is $0.11 per square foot, what is the cost of the cardboard used to
make the box?
2) A regulation volleyball has a volume of 303.74 cubic inches. The formula for the volume of the volleyball is
V 
4
3
r 3 where r = radius of the ball.
a) What is the radius of the ball? Solve algebraically.
b) What is the total surface area of the ball in square inches?
c) in square feet?
3) For the last snow fall of the winter a group of kids decide to make a snow fort in the shape of a square
pyramid. They want to pyramid to have a height of 10 feet and have a volume of 1000 cubic feet. The
1
formula for the volume of the box is V  L2  H where L = side length of the square base, and H = height
3
of the pyramid.
a) What is the side length of the pyramid? Solve algebraically.
a) Calculate the amount of snow they need to create the 4 walls of the pyramid. (Note: they will be
using the bare ground as the base.
c) Based on a 1 foot thickness to the walls, each square foot of snow will weight 12.5 pounds. What will
the total weight of the snow used to make the sides of the snow pyramid be?
4) An ice cream cone is made from 147.26 square centimeters of dough. The cone doesn’t need a base so all the
dough is used to make the lateral surface area, which has a slant height of 12.5cm. The formula for the LSA
1
of the cone is LSA  d  s where d = diameter of the cone and s = the slant height.
2
a) What is the diameter of the cone?
 
b) What is amount of ice cream that will fit inside of the cone?
5) Two possible designs for a new cereal are shown below. The company designing the box wants to test out two
different packaging designs. One design will be a rectangular prism, and the other will be a cylinder. The
total surface area of the box can be a maximum if 750 square inches.


a) The formula for the total surface area of the rectangular box is TSA  2 LW  LH  HW , width = 5.3
inches, and the length = 12 inches. Calculate the height of the box algebraically.
b) Calculate the volume of the rectangular box.
b) The formula for the total surface area of the cylindrical box is TSA  2rh
5.3 inches. Calculate the height of the box algebraically.
 2r 2 , and the radius =
CEREA
L
c) Calculate the volume of the cylindrical box.
d) Which of the boxes will hold more cereal? Explain why.