Algebra 1 Common Core Student Edition, Grade 8-9

Is th e re an o th er
way to solve the
problem?
Yes. You can set the
volumes equal to each
other and then solve
for h.

a 2 x — 5. y2- 16. 3 -9d d 3 — 3z

5 - 2x D ‘ 4 - y 1 Qd 2 + d - 1 ' 2 z 2 - 2

& Got It? 3. W hat is th e sim plified form of th e expression? State any excluded values.

You can use rational expressions to m odel som e real-w orld situations.

Problem 4 Using a Rational Expression

Shopping You are choosing between the two wastebaskets

that have the shape of the figures at the right. They both have

the same volume. What is the height h of the rectangular

wastebasket? Give your answer in terms of a.

Step 1 Find th e volum e of th e cylinder.

V = Trr2h Formula fo r volume o f a cylinder

= Tra2( 2a + 8 ) Substitute a fo r r and 2a + 8 for h.

Step 2 Find the height of a rectangular prism with volume Tra2( 2a + 8) an d

2 a + 8

2 a^2 a

base area B ■-

V = Bh

(2d)2 = 4 a 2

h =BV

va2(2a + 8 )

4a2

Tra2(2)(a + 4)

4a2

ird2\d)''(a + 4)

24142

v(a + 4)

Formula fo r volume o f a prism

Solve fo r h.

Substitute the volum e o f the cylinder fo r the volume o f the

rectangular prism and 4a 2 for B.

Factor.

Divide o ut common factors 2 and a2.

Simplify.

The height of th e rectangular prism isir(a + 4)

& G o t It? 4. a. A sq u are has side length 6x + 2. A rectangle w ith w idth 3x + 1 h as the

sam e area as th e square. W hat is th e length of th e rectangle?

b. Reasoning Suppose th e dim ensions of th e w astebaskets in Problem 4

are m easu red in feet. Is it possible for th e heig h t of th e rectangular

w astebasket to b e 1 ft? W hat are th e possible heights? Explain.

666 Chapter 11 Rat io nal Expressions and Funct ions