Question : If the circumference of a circle is equal to the perimeter of a square, and the radius of the given circle is positive, then which of the following options is correct?
Option 1: Area of the circle > Area of the square
Option 2: Area of the circle $\geq$ Area of the square
Option 3: Area of the circle < Area of the square
Option 4: Area of the circle = Area of the square
New: SSC MTS 2024 Application Form OUT; Direct Link
Don't Miss: Month-wise Current Affairs | Upcoming Government Exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: Area of the circle > Area of the square
Solution : Let the radius of the circle be '$r$' and side of the square be 'a' Since the perimeter of a square = circumference of a circle ⇒ 4a = 2$\pi r$ ⇒ a = $\frac{\pi r}{2}$ ⇒ Area of Square = $(\frac{\pi r}{2})^{2}$ ⇒ $\frac{\text{Area of circle}}{\text{Area of square}} = \frac{\pi r^{2}}{(\frac{\pi r}{2})^{2}}=\frac{4}{\pi}$ > 1 So, the area of the circle > the area of the square. Hence, the correct answer is Area of the circle > Area of the square.
Application | Cutoff | Selection Process | Preparation Tips | Eligibility | Exam Pattern | Admit Card
Question : The area of a square is 1296 cm2 and the radius of a circle is $\frac{7}{6}$ of the length of a side of the square. What is the ratio of the perimeter of the square and the circumference of the circle? [Use $\pi=\frac{22}{7}$ ]
Question : Directions: The areas of seven circles C1, C2, C3, C4, C5, C6, and C7 are compared. The area of C2 is greater than C5 and less than C1. The area of C4 is greater than C7 and less than C6. The area of C5 is more than C6. If the area of C7 is the lowest, then
Question : The side of a square is equal to 40% of the radius of a sphere. If the volume of the sphere is $\frac{500 \pi}{3} \mathrm{~m}^3$, then what is the area of the square?
Question : If the circumference of a circle is 13.2 cm, then what is its radius?
Question : Each side of a square is 12 cm long. The perimeter of this square is equal to the perimeter of a rectangle whose length is 16 cm. What will be the area of this rectangle?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile