Question

part 2

1. the perimeter of a rectangle is 48 centimeters. the relationship between the length (l), the width (w), and the perimeter of the rectangle can be described with the equation ( 2l + 2w = 48 ). find the length, in centimeters, if the width is:

a) 10 centimeters
b) 3 centimeters
c) ( w ) centimeters

1. ( v = pi r^2 h ) is an equation to calculate the volume of a cylinder, ( v ), where ( r ) represents the radius of the cylinder and ( h ) represents its height. which equation allows us to easily find the height of the cylinder because it is solved for ( h )?

a) ( r^2 h = \frac{v}{pi} )
b) ( h = v - pi r^2 )
c) ( h = \frac{v}{pi r^2} )
d) ( pi h = \frac{v}{r^2} )

Explanation:

Problem 2

Step1: Start with the volume formula

We have the volume of a cylinder formula \( V = \pi r^2 h \). We need to solve for \( h \).

Step2: Isolate \( h \)

Divide both sides of the equation by \( \pi r^2 \) to get \( h \) by itself. So, \( h=\frac{V}{\pi r^2} \).

Step1: Simplify the perimeter formula

Given the perimeter of a rectangle \( P = 2l+2w = 48 \). Divide both sides by 2: \( l + w=24 \).

Step2: Solve for length

Rearrange the equation to solve for \( l \): \( l = 24 - w \).
If we take option a) \( w = 10 \) cm:

Step3: Substitute width value

Substitute \( w = 10 \) into \( l = 24 - w \), we get \( l=24 - 10=14 \) cm.
If we take option b) \( w = 3 \) cm:

Step3: Substitute width value

Substitute \( w = 3 \) into \( l = 24 - w \), we get \( l=24 - 3 = 21 \) cm.
If we take option c) \( w \) cm:

Step3: Express length in terms of width

\( l=24 - w \) cm.

(Note: Since the original problem's question for part 1 is a bit unclear (maybe a multiple - choice with options a, b, c for width and we need to find length), the above is a general solution approach. If you can clarify the exact question for part 1, a more specific answer can be provided.)

Answer:

C) \( h = \frac{V}{\pi r^2} \)

Problem 1 (Assuming we need to solve for length for each width option, let's take option a) 10 cm first as an example, but since the question is a bit unclear on which width to use, maybe it's a multiple - choice with width options and we need to find length. Let's assume we solve for length \( l \) from \( 2l + 2w=48 \), simplify to \( l + w = 24 \), so \( l=24 - w \))