Answer:
a) A = (209.7 ± 5.0) cm^2
b) V = (251.6 ± 75.5) cm^3
Explanation:
The area will be simply
21.4 * 9.8 = 209.7 cm^2
For multiplication of uncertainties you have to first convert them to relative uncertainties
[tex]\frac{100 * 0.3}{21.4} = 1.4%[/tex]
[tex]\frac{100 * 0.1}{9.8} = 1.0%[/tex]
Then we add those together and this is the relative uncertainty of the product
(209.7 ± 2.4%) cm^2
And we can convert it to absolute uncertainty:
[tex]=\frac{2.4 * 209.7}{100} = 5.0[/tex]
Then the area is expressed as:
A = (209.7 ± 5.0) cm^2
For volume
209.7 * 1.2 = 251.6 cm^3
And the relative uncertainty is
[tex]\frac{100*0.3}{1.2} = 25%[/tex]
So the volume with relative uncertainty is:
(251.6 ± 30%) cm^3
And converting it to absolute uncertainty:
[tex]=\frac{30 * 251.6}{100} = 75.5[/tex]
V = (251.6 ± 75.5) cm^3
The area of the brick is [tex](209.7 \pm 5.1)\ cm^2[/tex], while the volume of the brick is [tex](251.7 \pm 69) cm^3[/tex]
The dimension of the plastic brick is given as:
Length = (21.4 ± 0.3) cm
Width = (9.8 ± 0.1) cm
The area of a rectangle is:
Area = Length * Width
So, we have:
[tex]Area = 21.4 * 9.8[/tex]
[tex]Area = 209.7[/tex]
The smallest dimension of the brick is:
Length = 21.1 i.e. 21.4 - 0.3
Width = 9.7 i.e. 9.8 - 0.1
So, the smallest area is:
[tex]Area = 21.1 * 9.7[/tex]
[tex]Area = 204.7[/tex]
The largest dimension of the brick is:
Length = 21.7 i.e. 21.4 + 0.3
Width = 9.9 i.e. 9.8 + 0.1
So, the largest area is:
[tex]Area = 21.7 * 9.9[/tex]
[tex]Area = 214.8[/tex]
Next, calculate the midpoint of the uncertain areas:
[tex]d = \frac{214.8 - 204.7}{2}[/tex]
[tex]d = 5.1[/tex]
Hence, the area of the brick is:
[tex]Area= (209.7 \pm 5.1)[/tex]
The thickness is given as: (1.2 ± 0.3)
So, the volume of the brick is:
[tex]Volume = 21.4 * 9.8 * 1.2[/tex]
[tex]Volume = 251.7[/tex]
The smallest thickness of the brick is 0.9 i.e. 1.2 - 0.3
So, the smallest volume is:
[tex]Volume = (209.7 - 5.1) * 0.9[/tex]
[tex]Volume = 184.2[/tex]
The largest thickness of the brick is 1.5 i.e. 1.2 + 0.3
So, the largest volume is:
[tex]Volume = (209.7 + 5.1) * 1.5[/tex]
[tex]Volume = 322.2[/tex]
Next, calculate the midpoint of the uncertain volumes:
[tex]d = \frac{322.2 - 184.2}{2}[/tex]
[tex]d = 69[/tex]
Hence, the volume of the brick is:
[tex]Volume = (251.7 \pm 69) cm^3[/tex]
Read more about areas and volumes at:
https://brainly.com/question/10171109
