The ratio of the length to the breadth of a rectangle is 3:2, and the area of the rectangle is 216 cm². If the circumference of a circle is 28 cm more than the perimeter of the rectangle, then find the area of the circle (in cm²).

Correct answer: 616

Solution

Let the rectangle sides be 3x and 2x. Then 6x^2 = 216, so x = 6 and the sides are 18 cm and 12 cm, giving perimeter 60 cm. The circle’s circumference is 88 cm, so its radius is 14 cm and area is 616 cm².

Related IBPS PO Quantitative Aptitude questions

There is a rectangular path just inside a rectangular park. The width of the path is 2 cm. If the length of the park is decreased by 4 cm, it becomes a square. The area of the rectangle is 1\(\tfrac{1}{3}\) times the area of the path. From the above information, which of the following can be found out? (i) Area of the path (ii) Length of the park (iii) Sum of the perimeter of the rectangular park and the perimeter of the path (both external and internal perimeter) A) only (ii) B) only (ii) and (iii) C) only (i) and (iii) D) all of the above E) only (iii)
A cylindrical vessel with radius 17.5 cm and height 18 cm is filled to 80% of its capacity with milk. If all the milk is transferred into 30 cuboidal vessels whose length and breadth are 7 cm and 3 cm respectively, find the height of each cuboidal vessel.
Directions for Questions 65–67: A man goes to a shop from his home at a speed of _____ km/h, and the time taken to reach the shop is _____ hours. After reaching there, he purchases a cylindrical jar of height such that its capacity is \(83259\text{ cm}^3\). He also purchases a conical vessel whose capacity is \(\frac{1}{27}\) of the cylindrical jar, and the height of the conical vessel is 14 cm. Note: The height of the conical vessel is four times the height of the cylindrical jar. Find the ratio of the radius of the cylindrical jar to the radius of the conical vessel.
Directions for Questions 68–69: Match Column I and Column II based on the given questions. Column I (i) \(X\) = Cone, volume of cone = \(1232\text{ m}^3\) (ii) \(Y\) = Cylinder, volume of cylinder = \(1848\text{ m}^3\) (iii) \(S\) = Square, which is inscribed in a circle Column II (A) Radius = 14 m (B) Radius = 7 m (C) Circumference of circle = 44 m 68. If the difference between the height of \(Y\) and the side of \(S\) is greater than 20 m, then which option is correct?
Another tank Z has a height 20% more than that of tank R and a radius 20% more than that of tank P. What is the sum of the curved surface areas of tanks P and Z together (approximately)?
A right circular cylindrical tank of radius \(r\) cm and height \(r+12\) cm contains milk. The entire quantity of milk is taken out from the cylindrical tank and poured into \(N\) hemispherical bowls such that each bowl is filled to its maximum capacity. The maximum capacity of each bowl is \(\frac{11\pi^3}{35}\) cm\(^3\). Which among the following values of \(N\) are possible? (\(r\) and \(N\) are positive integers) I. 6 II. 34 III. 25 IV. 19

⚔️ Practice IBPS PO Quantitative Aptitude free + battle 1v1 →