A carpenter was told to make a rectangular desk with top of dimension 50cm by 40cm. The carpenter actually made the desk 60cm by 35cm. (a) Calculate the per...
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A carpenter was told to make a rectangular desk with top of dimension 50cm by 40cm. The carpenter actually made the desk 60cm by 35cm.
(a) Calculate the percentage error in the (i) length and the breadth ; (ii) area of the table top.
(b) Find the product of the two errors in a(i).
Answer Details
Intended dimensions: 50 cm by 40 cm. Actual dimensions made: 60 cm by 35 cm.
Percentage error \(= \dfrac{|\text{actual} - \text{intended}|}{\text{intended}} \times 100\%\).
(a)(i) Length:
\[ \frac{|60 - 50|}{50} \times 100\% = \frac{10}{50} \times 100\% = 20\%. \]Breadth:
\[ \frac{|35 - 40|}{40} \times 100\% = \frac{5}{40} \times 100\% = 12.5\%. \](a)(ii) Area: intended area \(= 50 \times 40 = 2000\ \text{cm}^2\); actual area \(= 60 \times 35 = 2100\ \text{cm}^2\).
\[ \frac{|2100 - 2000|}{2000} \times 100\% = \frac{100}{2000} \times 100\% = 5\%. \](b) Product of the two errors in a(i):
\[ 20\% \times 12.5\% = 0.20 \times 0.125 = 0.025 = 2.5\%. \]Download The App On Google Playstore
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