Name: ___________________________________________________ Period: _____________
Unit 7: Area, Surface Area, and Volume
Section 7.1: Area and Perimeter
Find the area of each figure. For questions 13-15, find the area of the shaded region.
6 cm
1.
2. 9 yd
Geometry
Practice
3.
6 yd
10.4 m
6 cm
10.8 yd
5.5 m
10 cm
10 in.
4.
9 in.
5.
5m
2.5 in
6.
8 in.
5m
5.2 in
4.8 in
9m
7.
8.
9.
3 in
4.4 ft
3.2 ft
11 in
10.
5m
6 in.
12 cm
14 m
14.
15.
6
8 ft
6in
14
12
5 ft
4 ft
4 yd
16 cm
5 cm
16 m
2 in.
13.
12.
6.5 m
8 in.
7 yd
3 ft
11.
7 in.
13 yd
12
14
4in
5in
13 in
Section 7.2: Area of Regular Polygons
Find the area of each polygon. Leave your answer as a simplified radical AND round to the nearest hundredth.
1. an equilateral triangle with apothem 6 cm
2. a square with radius 18 ft
3. a regular hexagon with apothem 20 mm
4. a regular hexagon with apothem 12 cm
5. a square with radius 10 cm
6. an equilateral triangle with apothem 4 m
7.
8.
9.
20 cm
6 in
5 in
10.
12 in.
11.
3.2 in
12.
5.5 in
20 mm
Section 7.3: Area of Circles and Sectors
Find the circumference of each circle. Leave your answers in terms of 𝝅 and round to the thousandth place.
1.
2.
16 ft
16 in
Find the length of each darkened arc. Leave your answers in terms of 𝝅 and round to the thousandth place.
3.
4.
9 in
120°
90°
5.
6.
20 m
30°
45°
Find the area of each circle. Leave your answers in terms of 𝝅 and round to the thousandth place.
7.
8.
16 in
16 ft
Find the area of each shaded sector of a circle. Leave your answers in terms of 𝝅 and round to the
thousandth place.
9.
10.
45°
45°
3 cm
2 ft
11.
12.
45°
6m
5 yd
60°
5 yd
Section 7.4: Surface Area
Find the surface area of each figure. Round to the nearest thousandth and leave in terms of 𝝅.
1.
2.
3.
5 in
12 ft
24 in
14 ft
4.
5m
12 ft
6 cm
10 m
7m
5.
6.
9 cm
7.
12 m
8.
3m
8 cm
4 yd
6m
9m
10.
6 cm
6 cm
11.
15 m
9.
9 cm
4 cm
12.
8 cm
13.
3 cm
4 cm
10 in
12 cm
2 cm
Section 7.5: Volume
Find the volume. Leave answers in terms of 𝝅 and round to the thousandth place.
1.
2.
9 cm
8 cm
3.
5 in
24 in
4.
5m
6 cm
10 m
7m
5.
6.
7.
12 m
4 yd
10 in
10 m
8.
8 cm
9.
4 ft
3 cm
4 cm
12 cm
8 ft
2 cm
3 ft
2 ft
6 ft
10.
11.
13 m
15 in
12 in
10 m
10 m
10 m
11 in
6 in
Section 7.6: Cross Sections and Applications
1.  If the radius of a sphere is doubled, what happens to the volume? If the radius is tripled?
2.  If you double the radius and triple the height of a cylinder, what will be the ratio of the cylinder’s original volume to the
cylinder’s new volume?.
3.  A cylindrical container with a radius of 12 centimeters is filled to a height of 6 centimeters with coconut oil. The density of coconut
oil is 0.92 gram per cubic centimeter. What is the mass of the coconut oil to the nearest gram?
4.  The Pyramid Arena in Memphis, Tennessee is about 98 meters tall and has a square base with a side length of about 180 meters.
A prism-shaped building has the same square base as the Pyramid Arena. What is the height of the building if it has the same
volume as the Pyramid Arena?
5.  You buy a friend a basketball as a gift. You want to construct a container to put
the ball in to disguise it when it is wrapped. You construct the two containers shown
in the diagram. Find the surface area of each container. Do the containers have the
same surface area as the ball? If not, which container has a surface area that is
closer to that of the ball?
Find the value of the variable. Use 3.14 for 𝝅.
6.
7.
The figures are similar. Find the volume of the figure B.
9.
10.
8.
11.
For each pair of similar figures, the area of the smaller figure is given. Find the area of the larger figure.
12.
13.
14.
Use Euler’s Formula to find the missing number for each polyhedron.
15. Faces: 5 and Vertices: 5
16. Edges: 9 and Vertices: 6
17. Faces: 8 and Edges: 18
Unit 7 FSA Practice Questions
1. 
The trunk of a palm tree has cylindrical tubes that carry water. Each tube is 0.0003 meters wide. One of
the tubes in a palm tree trunk is shown.
A. Using the diagram as a model, approximately how many tubes could fit in a palm tree trunk with a
diameter of 0.5 meters?
B. The tubes in a palm tree are between 20 to 21 meters long. What is the approximate volume, in cubic
meters, of one tube?
2.  Alejandro cut a circle with circumference C and radius r into 8 congruent sectors and use them to make the figure shown.
Alejandro notices that the figure was very close to the shape of a parallelogram. Select all the statements that apply to the
figure.
A. The height of the parallelogram is approximately equal to the circle’s diameter.
B. The area of the parallelogram is approximately 1/2Cr
C. The length of the parallelogram is approximately equal to the circle’s circumference
D. The radius of the circle is approximately equal to the height of the parallelogram
E. The area of the parallelogram is approximately 8(45/360𝜋r2)
3. 
The population of Florida in 2010 was 18,801,310 and the land area was 53,625 square miles. The population increased 5.8% by 2014.
A.  To the nearest whole number, what is the population density, in people per square mile, for Florida in 2014?
B.  To the nearest whole number, how much did the population density, in people per square mile, increase from 2010 to 2014?
4.  As phosphate is mined, it moves along a conveyor belt, falling off of the end of the belt into the shape of a right circular cone. A
shorter conveyor belt also has phosphate falling off of the end into the shape of a right circular cone. The height of the second
pile of phosphate is 3.6 feet shorter than the height of the first. The volume of both piles is the same. To the nearest of a foot,
what is the diameter of the second pile of phosphate?
5.  A rectangle and a horizontal line segment are shown. What is the resulting object when the rectangle is rotated around the
horizontal line segment?
A.
B.
C.
D.
Name: ___________________________________________ Date: __________
Unit 7 Test: Measuring Figures and Solids
PRACTICE
Directions: Show ALL of your work for every problem. Circle your answers.
TEST
Find the surface area and volume for each figure. Round to the nearest hundredth.
1.
2.
3.
4.
5.
6.
Find the area for each figure. Round to the nearest hundredth.
7.
8.
9.
10.
11.
12.Find the area of the shaded region
13. Find the circumference of the entire circle.
15. Find the area of the entire circle.
10
120°
12 in
14. Find the length of the darkened arc.
135°
16. Find the area of the shaded region.
The figures in each diagram are similar.
•  For two-dimensional figures, find the ratio of their areas and the unknown area.
•  For three-dimensional figures, find the ratio of their volumes and the unknown volume.
13. Area of larger = 72 ft2
14. Volume of smaller = 135 cm3
Solve each word problem. Show all work and round answers to the nearest hundredth.
15.  A small box holds 20 oz of cereal. The family size box is formed by scaling the
dimensions of the small box by a factor of 9/8. How much more cereal can the family
size box hold? Round to the nearest hundredth.
16.  Jason is designing a label for a water bottle. What is the area of the label if the bottle
is 10 in tall and has a radius of 5 in?
17. 
Mr. Williams is building a sand box for his children. It costs $320 for the sand if he builds
a sand box with dimensions 9 ft by 6 ft. How much will the sand cost if Mr. Williams
decides to increase the size to 15 ft by 10 ft?