Question

The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10 cm long now measures 9 cm. The area of the reduced plan is measured as 81 $c{m}^2.$ The actual area $\left(m^2\right)$ of the survey is

• A. 10000
• B. 6561
• C. 1000
• D. 656

Answer 1

The correct option is A 10000

Actual area of survey
$={\left(\frac{\text{Actual scale}}{\text{Reduced scale}}\right)}^2\times \text{Measured plan area}\times (scale{)}^2$
$={\left(\frac{10}{9}\right)}^2\times 81\times {\left(\frac{10m}{1cm}\right)}^2$
$={\left(\frac{10}{9}\right)}^2\times 81\times {\left(\frac{1000}{1}\right)}^2$
$={10}^{8}c{m}^2={10}^4{m}^2=10000m^2$