Question:
Rekha drew a circle of radius 2 cm on a graph paper of grid 1 cm × 1 cm. She then calculated the area of the circle by adding up only the number of full unit-squares that fell within the perimeter of the circle. If the value that Rekha obtained was 4 sq cm less than the correct value, then find the minimum possible value of \(d\).
Rekha drew a circle of radius 2 cm on a graph paper of grid 1 cm × 1 cm. She then calculated the area of the circle by adding up only the number of full unit-squares that fell within the perimeter of the circle. If the value that Rekha obtained was 4 sq cm less than the correct value, then find the minimum possible value of \(d\).
Show Hint
Area underestimation from digitization often yields approximations closer to integer-covered regions. Estimate the reduced area directly.
Updated On: Jul 28, 2025
- 6.28
- 7.28
- 7.56
- 8.56
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Correct area of circle
Radius \(r = 2\) cm. \[ \text{Area} = \pi r^2 = \pi \cdot 4 \approx 12.56 \text{ sq cm} \] Step 2: Rekha’s estimated area
She underestimated by 4 sq cm, so: \[ \text{Her estimate} = 12.56 - 4 = 8.56 \text{ sq cm} \] Since the circle is being approximated using unit squares, and this estimation is dependent on resolution of grid (i.e., grid size = 1 cm), the effective resolution error is related to the perimeter. Step 3: Area underestimation indicates coarser circle sampling.
We must estimate what value of \(d\) could result in an estimate of 8.56. Since radius is fixed, this is a distractor: The correct value is the under-estimate Rekha got: \[ \boxed{8.56} \]
Radius \(r = 2\) cm. \[ \text{Area} = \pi r^2 = \pi \cdot 4 \approx 12.56 \text{ sq cm} \] Step 2: Rekha’s estimated area
She underestimated by 4 sq cm, so: \[ \text{Her estimate} = 12.56 - 4 = 8.56 \text{ sq cm} \] Since the circle is being approximated using unit squares, and this estimation is dependent on resolution of grid (i.e., grid size = 1 cm), the effective resolution error is related to the perimeter. Step 3: Area underestimation indicates coarser circle sampling.
We must estimate what value of \(d\) could result in an estimate of 8.56. Since radius is fixed, this is a distractor: The correct value is the under-estimate Rekha got: \[ \boxed{8.56} \]
Was this answer helpful?
0
0
Top CAT Quantitative Aptitude Questions
- In a triangle ABC,AB=AC=8cm. A circle drawn with BC as diameter passes through A. Another circle drawn with center at A passes through B and C. Then the area,in sq.cm,of the overlapping region between the two circles is
- The simple interest accrued on an amount of Rs.25,000 at the end of three years is Rs.7,500. What would be the compound interest accrued on the same amount at the same rate in the same period?
- What is the sum of all roots of the equation \(|x+4|^2–10|x+4|=24\)?
- A solid metal sphere is melted and smaller spheres of equal radii are formed. 10% of the volume of the sphere is lost in the process. The smaller spheres have a radius which is \(\frac{1}{9}\text{th}\) the larger sphere. If 10 litres of paint were needed to paint the larger sphere,how many litres are needed to paint all the smaller spheres?
- The ratio of the ages of a husband and his wife when they got married was 6:5. 4 years and 6 years after their marriage they had their 1st and 2nd children. The sum of the present ages of the husband and wife is 6.4 times the sum of the present ages of their children. The average age of the family at present is 18.5 years. Find the ratio of the ages of the husband and wife when their second child was born.
View More Questions
Top CAT Geometry Questions
In the figure, \(O\) is the centre of the circle and \(AC\) is the diameter. The line \(FEG\) is tangent to the circle at \(E\). If \(\angle GEC = 52^\circ\), find the value of \(\angle E + \angle C\).
- Rekha drew a circle of radius 2 cm on a graph paper of grid 1 cm × 1 cm. She then calculated the area of the circle by adding up only the number of full unit-squares that fell within the perimeter of the circle. If the value that Rekha obtained was 4 sq cm less than the correct value, then find the minimum possible value of d.
what is the minimum possible value of \(d\)? - A rectangle is drawn such that none of its sides has length greater than ‘\( a \)’. All lengths less than ‘\( a \)’ are equally likely. The chance that the rectangle has its diagonal greater than ‘\( a \)’ (in terms of %) is:
- A solid sphere of radius 12 inches is melted and cast into a right circular cone whose base diameter is \( \sqrt{2} \) times its slant height. If the radius of the sphere and the cone are the same, how many such cones can be made and how much material is left out?
- The side of an equilateral triangle is 10 cm long. By drawing parallels to all its sides, the distance between any two parallel lines being the same, the triangle is divided into smaller equilateral triangles, each of which has sides of length 1 cm. How many such small triangles are formed?
View More Questions
Top CAT Questions
- Compare and contrast between Portia and Jessica characters in Merchant of Venice.
- In a triangle ABC,AB=AC=8cm. A circle drawn with BC as diameter passes through A. Another circle drawn with center at A passes through B and C. Then the area,in sq.cm,of the overlapping region between the two circles is
- The simple interest accrued on an amount of Rs.25,000 at the end of three years is Rs.7,500. What would be the compound interest accrued on the same amount at the same rate in the same period?
- What is the sum of all roots of the equation \(|x+4|^2–10|x+4|=24\)?
- A solid metal sphere is melted and smaller spheres of equal radii are formed. 10% of the volume of the sphere is lost in the process. The smaller spheres have a radius which is \(\frac{1}{9}\text{th}\) the larger sphere. If 10 litres of paint were needed to paint the larger sphere,how many litres are needed to paint all the smaller spheres?
View More Questions