Question

Find the volume of a block whose measurement are(7.85+-0.3)m(2.98+-0.1)m and(5.38+-0.2)m

Answer 1

We know that

Volume = Length*Breadth*Height

Now,

A very basic rule of units and dimensions is that :-

Error is always Added.

$\rule{200}{2}$

L= $7.85\pm0.3$

B= $2.98\pm0.1$

H= $5.38\pm0.2$

$\rule{200}{2}$

Also,

$\dfrac{\triangle V}{V}=\dfrac{\triangle H}{H}+\dfrac{\triangle L}{L}+\dfrac{\triangle B}{B}$

Where, dell V, dell L, dell H and dell B are the change or errors in Volume, Length, Height and Breadth respectively.

$\rule{200}{2}$

$7.85 \times 2.98 \times 5.38 = 125.85$

Applying the formula :-

$\dfrac{\triangle V}{125.85}=\dfrac{0.3}{7.85}+\dfrac{0.1}{2.98}+\dfrac{0.2}{5.38}\\ \\ \\ \triangle V= 125.85(0.038+0.034+0.037)\\ \\ \\ \triangle V= 125.85×0.109\\ \\ \\ \triangle V=13.718$

$\rule{200}{2}$

Thus,

The error in the Volume is equal to 13.718 metres.

Thus,

Volume of the block can be expressed as :-

$= 125.85 \pm13.718 \: \: metres$

$\rule{200}{2}$