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%.