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
- 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? - The area of a triangle is 20 cm^2. The height is 3 cm more than its base.
What are the base and height? - 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? - 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? - 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? - 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
- The area of a triangle is 12 in
height. What are the base and height?
PRACTICE
- The area of a triangle is 12 in