1 Sq. mile = $10^9$ Sq. centimetres
Surface Measure Conversions: Identifying the Incorrect Statement
This question requires identifying the incorrect statement among the given conversion factors for 1 Square mile. We will verify each option.
Verification of Surface Measure Conversions
-
Option 1: 1 Sq. mile = 2.590 Sq. kilometres
A mile is approximately 1.60934 kilometres. Squaring this gives:
$1 \text{ Sq. mile} = (1.60934 \text{ km})^2 \approx 2.589988 \text{ Sq. km}$
Rounded to three decimal places, this is 2.590 Sq. km. Thus, this statement is correct. -
Option 2: 1 Sq. mile = 259 Hectares
Since 1 Sq. km equals 100 Hectares, and we know 1 Sq. mile is approximately 2.590 Sq. km:
$1 \text{ Sq. mile} \approx 2.590 \times 100 \text{ Hectares} = 259 \text{ Hectares}$
This statement is correct. -
Option 3: 1 Sq. mile = 640 Acres
This is a standard and well-established conversion factor used in land measurement.
This statement is correct. -
Option 4: 1 Sq. mile = $10^9$ Sq. centimetres
First, convert 1 mile to centimetres:
$1 \text{ mile} = 1.60934 \text{ km} = 1609.34 \text{ m} = 160934 \text{ cm}$
Now, calculate the area in square centimetres:
$1 \text{ Sq. mile} = (160934 \text{ cm})^2 = 25,899,983,742.2 \text{ Sq. cm}$
The value $10^9$ Sq. cm is $1,000,000,000$ Sq. cm.
Comparing the calculated value with the given value: $25,899,983,742.2 \neq 1,000,000,000$.
Therefore, this statement is incorrect.
Final Conclusion
Based on the calculations, the statement claiming 1 Sq. mile equals $10^9$ Sq. centimetres is not correct.
Important Questions from Numerical Computation
Ratio of the angles of a triangle are 1 : 2 : 6. What is the smallest angle?
It would take one machine 4 hours to complete a production order and another machine 2 hour to complete the same order. If both machines work simultaneously at their respective constant rates, the time taken to complete the same order is ________ hours.
Two design consultants, P and Q, started working from 8 AM for a client. The client budgeted a total of USD 3000 for the consultants. P stopped working when the hour hand moved by 210 degrees on the clock. Q stopped working when the hour hand moved by 240 degrees. P took two tea breaks of 15 minutes each during her shift, but took no lunch break. Q took only one lunch break for 20 minutes, but no tea breaks. The market rate for consultants is USD 200 per hour and breaks are not paid. After paying the consultants, the client shall have USD_remaining in the budget.
What is the value of \(1 + \frac{1}{4} + \frac{1}{{16}} + \frac{1}{{64}} + \frac{1}{{256}} + \ldots ?\)
A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of the shadow is twice her height. What is the height of the lamp post in meters?
