Question

The area of the plan of a survey plotted to a scale of 15 m to 1 cm measures as 80.2 $c{m}^2$ as found by a planimeter. The plan is found to have shrunk so that a line originally 10 cm long now measures 9.8 cm only. The shrunk scale and true area of the survey respectively are

• A. 15.3 m to 1 cm, 18788.74 m${}^2$
• B. 15.3 m to 1 cm, 770231.23cm${}^2$
• C. 14.7 m to 1 cm 77.02 cm${}^2$
• D. 15.3 m to 1 cm, 83.51 cm${}^2$

Answer 1

The correct option is A 15.3 m to 1 cm, 18788.74 m${}^2$

$S.F=\frac{Shrunklength}{Originallength}=\frac{9.8}{10}=0.98$

Original scale is 1 cm = 15 m

$\therefore Shrunkscale=S.F\times Originalscale$

$=0.98\times \frac{1}{15}=\frac{1}{15.306}m$

$1c{m}^2=15.306m^2$

$\therefore Correctarea=80.2\times (15.306{)}^2$

$=18788.74m^2$