Key
Math 8
Unit 3: Geometric Applications of Exponents – Study Guide
1.
2.
3.
The Pythagorean Theorem states that the square of the
length of the hypotenuse is equal to the sum of the
squares of the lengths of the legs.
The Pythagorean Theorem can be represented by the
2
2 2
equation a +b =c , where a and b are the length of the
legs of the triangle, and c is the length of the
hypotenuse.
Use what you know about the Pythagorean Theorem to
label the sides of the following triangle.
leg
Date ________________
7.
A rectangle has a diagonal 25 inches long and a width of
6 inches. What is the length of the rectangle?
24 inches
8.
Which of the following measures are valid
measures of the sides of a right triangle? Explain
your reasoning.
A. 3, 4, 7
B. 5, 12, 13
C. 20, 21, 28
D. 12, 37, 34
hypotenuse
They form a true statement when plugged into the
2
2
2
formula a +b = c
leg
4.
Is a triangle with the lengths 7, 24, and 25 a right
triangle. Why or why not. Show work to indicate how
you got your answer.
2
2
2
7 + 24 = 25
49 + 576 = 625
625 = 625, so yes it is a right triangle. Using the
2
2
2
Pythagorean Theorem, a +b = c , the numbers form a
true statement
5.
A football field is 360 feet by 45 feet. How long is the
walk from one corner diagonally to the opposite
corner?
9. A spider has taken up residence in a small
cardboard box which measures 2 inches by 4
inches by 4 inches. What is the length, in inches,
of a straight spider web that will carry the spider
from the lower right front corner of the box to the
upper left back corner of the box?
452 + 3602 = c2; 2025 + 129600 = 131625
= 362.8; The walk is 362.8 ft2
√
6.
Using the illustration below, what is the approximate
height of the hot air balloon?
√
= 6 inches
10. A package is in the shape of a cube. The height if
the package is 10 inches. What is the diagonal
length of the package?
√
2
2
2
2
a + 1325 = 2000 ; a =2244375; the height is approx..
2
1498 ft
= 17.3 inches
11. Find the length of the missing side.
X
18. A party hat is in the shape of a cone with a radius
of 3 in. and a height of 5 in. What is the volume of
the party hat?
47.1 in3; use V=
3 in.
19. What is the volume of a beach ball with a radius
of 12 centimeters?
5 in.
7234.56 cm3; use V =
5.8 in.
20. What is the volume of the following cone?
10 mm
12. Solve for y: 2
y=2
= 16
13. Solve for z: 3
z=6
= 108
5 mm
130.8 mm3
14. Explain what the word volume means.
21. Find the volume of the sphere shown below.
Radius is 2in
15. How does the volume of a cylinder compare to the
volume of a cone?
the volume of a cylinder is three times that of a
cone
16. How does the volume of a cylinder and cone
compare to the volume of a sphere?
33.49 in3
22. Find the volume of the cylinder below.
7 in
5 in
17. A candle maker uses a cylinder mold, which is 18
inches tall and has a radius of 1 inch. What is the
volume of the candle mold?
56.52 in3; use V= 2h
137.38 in3
23. The volume of a cylinder is 12.56
. If the height
of the cylinder is 1 m, what is its diameter?
Hint: Work backward on this one.
; substitute the information you
know in order to solve.
diameter = 4
26. What is the distance between P1 and P2?
5
24. What are the two methods of finding the distance
between two points?
25. What is the distance between P1 and P2?
10.8
27. Given points C(-6, 10) and D(-3, -2), what is the
length of CD?
12.37 (hint, use the Pythagorean theorem)
28. Given points S(-4, -2 and T(-1, 0), what is the
length of ST?
3.6 (hint, use the Pythagorean theorem)