# What is the percentage reduction in area of aluminum rod?

## What is the percentage reduction in area of aluminum rod, initial diameter 0.8 in and final diameter at fractured section 0.7 in?

1 .2.5%

2. 20.4%

3. 23.4%

4. 14.3%

## The percentage reduction in area of the aluminum rod is approximately 23.5%. The closest answer option is 23.4%.

To find the percentage reduction in area of the aluminum rod, we can use the formula:

% reduction in area = ((initial area - final area)/initial area) x 100%

We first need to calculate the initial and final areas of the aluminum rod based on the given diameters:

Initial diameter = 0.8 in

Initial radius = 0.8/2 = 0.4 in

Initial area = π(0.4)^2 = 0.5027 in^2

Final diameter = 0.7 in

Final radius = 0.7/2 = 0.35 in

Final area = π(0.35)^2 = 0.3848 in^2

Now, we substitute these values into the formula for % reduction in area:

% reduction in area = ((0.5027 - 0.3848)/0.5027) x 100%

% reduction in area = (0.1179/0.5027) x 100%

% reduction in area = 23.5%

Therefore, the percentage reduction in area of the aluminum rod is approximately 23.5%. The closest answer option is 23.4%.