Exercise 28 Page 289

Side Length (s)	Volume (V)
2	8
4	64
8	512
16	4096

Practice makes perfect

a Let's consider a cube with a side length of s.

In this part, we will sketch a model of cubes with side lengths of 2, 4, 8, and 16 units.

b We use the formula shown below to find the volume of a cube with a side length of s.

V=s^3 Let's apply the formula and complete the table.

Side Length (s)	V=s^3	Volume (V)
2	V=( 2)^3	V=8
4	V=( 4)^3	V=64
8	V=( 8)^3	V=512
16	V=( 16)^3	V=4096

c Let's first determine the rate of change by looking at the table.

Change in (s)	Side Length (s)	Volume (V)	Change in (V)
	2	V=8
*2 ↪	4	V=64	*8 ↩
*2 ↪	8	V=512	*8 ↩
*2 ↪	16	V=4096	*8 ↩

Now, we can make our conjecture.

Conjecture
When the side length of a cubed is doubled, the volume of the cube is multiplied by 8.

d In this part, we will write our conjecture as an algebraic expression.

Conjecture When the side length of a cubed is doubled, the volume of the cube is multiplied by 8. Algebraic Expression ( 2s)^3= 8V

e Let's prove our conjecture from Part D. To write any proof, we should begin by stating the given information and what we want to prove.

Given: s^3=V Prove: (2s)^3=8V Next, we will multiply both side of the equation by 8 using the Multiplication Property of Equality.

Multiplication Property of Equality 8s^3= 8V As a final step, we will take the cube root of the left-hand side by the Cube Root Property of Equality. Cube Root Property of Equality ( 2s)^3= 8V Combining these steps, we can create our two-column proof.

Statements	Reasons
1. s^3=V	1. Given
2. 8s^3= 8V	2. Multiplication Property of Equality
3. 2^3* s^3= 8V	3. Substitution Property of Equality
4. ( 2s)^3= 8V	4. Substitution Property of Equality

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Exercises p.287-291

Exercise 28 Page 289

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