Algebra Demystified 2nd Ed

Chapter 11 QuaDraTiC appliCaTionS 425

Let x represent the cup’s current radius. Then the radius of the new cup
would be x + 1. The volume formula becomes 169.6 = o(x + 1)^2 6.

169616

1696

6

1 1696

6

9

9

2

2

.()

. ().

(

=+

=+  ≈







=

o

oo

x

x

x++

=+ +

=++

=+−

=− +

1

911

921

028

024

2

2

2

)

()()

()()

xx

xx

xx

xx

x – 2 = 0 x + 4 = 0 (This does not lead to a solution.)

x = 2

The cup’s current radius is approximately 2 inches.

PRACTICE

1. The area of a triangle is 12 in^2. The length of its base is two-thirds its
   height. What are the base and height?


2. The area of a triangle is 20 cm^2. The height is 3 cm more than its base.
   What are the base and height?


3. The sum of the base and height of a triangle is 14 inches. The area is
   20 in^2. What are the base and height?


4. The hypotenuse of a right triangle is 85 cm long. One leg is 71 cm longer
   than the other. What are the lengths of its legs?


5. The manufacturer of a food can wants to increase the capacity of one of
   its cans. The can is 5 inches tall and its diameter is 6 inches. The manu-
   facturer wants to increase the can’s capacity by 50% and wants the can’s
   height to remain 5 inches. How much does the diameter need to
   increase?


6. A pizza restaurant advertises that its large pizza is 20% larger than the
   competition’s large pizza. The restaurant’s large pizza is 16" in diameter.
   What is the diameter of the competition’s large pizza?

PRACTICE

1. The area of a triangle is 12 in
   height. What are the base and height?

PRACTICE

1. The area of a triangle is 12 in