Answer:
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%
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