Geometry
REVIEW ch 12
Name ____________________________________________
S prism/cylinder = Ph + 2B
V prism/cylinder = Bh
S pyramid/cone = ½ Pl + 2B
V pyramid/cone = 1/3 Bh
S sphere = 4πr2
V sphere = (4/3)πr3
1) In a solid cone, the base has a radius of 7 units and is sliced in half vertically from the top point.
a) What is the shape of the cross section?
b) What is the length of the base of the cross section?
c) If the area of the cross section created is 168 units2, approximately what is the height of the cross
section?
2) You are getting ready to eat a delicious sandwich you just made. The bread is rectangular with
a length of 6 inches and a width of 8 inches. You stacked the sandwich so it is 2 inches tall.
Before you eat it though, you like to cut your sandwich diagonally.
a) What is the length of the diagonal of the sandwich?
b) What is the shape of the cross section made by the diagonal cut?
Draw the shape and label the known side lengths.
c) Find the area of the cross section formed.
3) The dimensions of Bria’s camping tent are shown in the diagram below.
a) How much fabric is needed to make the entire tent?
b) The tent is not waterproof, so Bria wants to put a tarp over it in case it rains. The tarp will
cover two of the tent’s rectangular faces. Which size tarp should she buy - the one that is 50
feet2, 100 feet2, or 150 feet2.
S prism/cylinder = Ph + 2B
V prism/cylinder = Bh
S pyramid/cone = ½ Pl + 2B
V pyramid/cone = 1/3 Bh
S sphere = 4πr2
V sphere = (4/3)πr3
4) For Father’s Day, you decide to build your dad a bird house in the shape of a hexagonal
pyramid. If you want each side of the base to have a length of 10 inches and a slant height of
15 inches, what is the total area of the materials you will need for the bird house? Round to the
nearest hundredth.
5) The cylindrical glass is full of water and then poured into the rectangular pan.
a) How much water will fit in the pan?
15 cm
b) How much water will fit in the glass?
Round the nearest hundredth.
8 cm
10 cm
5 cm
15 cm
c) Will the water overflow when poured into the pan?
Why or why not?
6) Cone Country Ice Cream Shoppe has mini cones with a diameter of 4 cm and a height of 4 cm.
Cone Country wanted to make a bigger cone that will hold 2.5 times more ice cream.
a) What is the volume of the mini cone? Leave answer in terms of pi.
b) What will the volume be of the large cone? Leave answer in terms of pi.
c) If the diameter remains the same, find the height of the large cone.
Round to the nearest centimeter.
S prism/cylinder = Ph + 2B
V prism/cylinder = Bh
S pyramid/cone = ½ Pl + 2B
V pyramid/cone = 1/3 Bh
S sphere = 4πr2
V sphere = (4/3)πr3
7) The top of a roof in the shape of a square pyramid has a base side length of 12 yards and is 1.6
times the height of a smaller square pyramid with the same base side length.
a) If the volume of the smaller roof is 240 yd3, what is the height of the smaller roof?
b) What is the height of the larger pyramid shaped roof?
c) What is the volume of the larger pyramid?
8) A baseball has a radius of approximately 1.5 centimeters while a basketball has a diameter of
approximately 9 centimeters.
a) What is the surface area of the basketball? Leave answer in terms of pi.
b) What is the surface area of the baseball? Leave answer in terms of pi.
c) How does the surface area of a basketball compare to the surface area of a baseball? Be very
specific. (Example Answer: The surface area of the basketball is 2.5 times bigger than the surface
area of the baseball.)
9) You need to paint a child’s toy that is made up of a cylinder and hemisphere, as shown below.
The radius of the cylinder is 14 cm and its altitude measures 30 cm.
a) What is the surface area of the cylinder? (Keep in mind the “top base” is not on the surface
anymore!) Leave answer in terms of pi.
b) What is the surface area of the hemisphere? (Keep in mind the “base” is not on the surface
anymore!) Leave answer in terms of pi.
c) What is the total surface area of the child’s toy? Round to the nearest hundredth.
30 cm
d) If a small paint can covers 2000 cm2, how many cans are needed to paint the surface if it 14 cm
requires two coats?
S prism/cylinder = Ph + 2B
V prism/cylinder = Bh
S pyramid/cone = ½ Pl + 2B
V pyramid/cone = 1/3 Bh
S sphere = 4πr2
V sphere = (4/3)πr3
10) You have mastered solving a Rubik’s Cube. Now, you’re looking for a challenge and have
discovered a spherical Rubik’s Cube.
a) If the traditional Rubik’s Cube has a volume of 185.193 cubic centimeters, what is the measure
of the length, width, and height?
b) If the spherical Rubik’s Cube could fit inside the traditional Rubik’s Cube, what is the maximum
diameter of the spherical Rubik’s Cube ?
c) What is the surface area of the spherical Rubik’s Cube? Round to the nearest hundredth.
11) Mr. Thurlwell’s hall pass (wooden block) is in need of a new paint job. What should you use
to determine how much paint is needed to cover the block? Specify if you should use surface
area or volume and what type of shape you should use.
12) You need to fill the pool up with water. How would you determine how much water is
needed to fill up the pool? Assume that the ends are semi-circles. Specify if you should use
surface area or volume and what type of shapes you should separate the pool into.