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blevinsiman
08.11.2019 •
Mathematics
The edge of a cube was found to be 30 cm with a possible error in measurement of 0.5 cm. use differentials to estimate the maximum possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (round relative errors to four decimal places and percentage errors to two decimal places.)max error relative error percentage errorvolume cm^3 %surface area cm^2 %
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Ответ:
for the volume a cube
Possible error = 1350cm³
Relative error = 0.05
Percentage error = 5%
For the surface area of a cube
Possible error = 180cm²
Relative error = 0.0333
Percentage error = 3.33%
Step-by-step explanation:
A cube is a three dimensional solid object with six (6) faces, twelve (12) edges and eight(8) vertices.
The volume of a cube = x³
Where x= length of the edge of a cube
X = 30cm 0.5cm
Differentiate V with respect to x (V = Volume of a cube)
dV/dx= 3 x²
dV= 3 x² . dx
dV = 3 × 30² × (0.5)
dV= 2700(0.5)
= 1350cm³
Maximum possible error = 1350cm³
Relative error = possible error /Volume
= dV/V
Recall that V = x³
V= (30)³
A = 27000cm³
Substitute the values for and V into the formula for Relative error
Relative error = 1350/27000
Relative error = 0.05
% error = Relative error × 100
= 0.05× 100
= 5%
Surface Area of a cube = 6x²
A = 6x²
Differentiate A with respect to x
dA/dx = 12x
dA/dx = 12x . dx
= 12 × 30 (0.5)
= 180cm²
Maximum possible error = 180cm²
Relative error = possible error / surface area
= dA/A
Recall that A = 6x²
A = 6(30)²
A = 5400cm²
Substitute the values for and A into the formula for Relative error
Relative error = 180/5400
Relative error = 0.0333(4 decimal place)
% error = Relative error × 100
= 0.0333 × 100
= 3.33%
Ответ:
The mean absolute deviation of this set is 3.43 or 3. Have a good day!