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# CAT Previous Year Questions: Mensuration - Notes | Study Quantitative Aptitude (Quant) - CAT

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Question for CAT Previous Year Questions: Mensuration
Try yourself:From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, is



Question for CAT Previous Year Questions: Mensuration
Try yourself:If a rhombus has area 12 sq cm and side length 5 cm, then the length, in cm, of its longer diagonal is



Question for CAT Previous Year Questions: Mensuration
Try yourself:The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side. P is the midpoint of CD and ABPD is a parallelogram. If the difference between the areas of the parallelogram ABPD and the triangle BPC is 10 sq cm, then the area, in sq cm, of the trapezium ABCD is



*Answer can only contain numeric values
Question for CAT Previous Year Questions: Mensuration
Try yourself:Let D and E be points on sides AB and AC, respectively, of a triangle ABC, such that AD : BD = 2 : 1 and AE : CE = 2 : 3. If the area of the triangle ADE is 8 sq cm, then the area of the triangle ABC, in sq cm, is



Question for CAT Previous Year Questions: Mensuration
Try yourself:Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipe B drains it. If pipe A is opened at 2 pm and pipe B is opened at 3 pm, then the tank becomes full at 10 pm. Instead, if pipe A is opened at 2 pm and pipe B is opened at 4 pm, then the tank becomes full at 6 pm. If pipe B is not opened at all, then the time, in minutes, taken to fill the tank is



Question for CAT Previous Year Questions: Mensuration
Try yourself:The cost of fencing a rectangular plot is ₹ 200 per ft. along one side, and ₹ 100 per ft along the three other sides. If the area of the rectangular plot is 60000 sq. ft, then the lowest possible cost of fencing all four sides, in INR, is



*Answer can only contain numeric values
Question for CAT Previous Year Questions: Mensuration
Try yourself:A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of ₹125 per m, is



Question for CAT Previous Year Questions: Mensuration
Try yourself:If a triangle ABC, ∠BCA=50o . D and E are points on AB and AC, respectively, such that AD=DE. If F is a point on BC such that BD=DF , then ∠FDE, in degrees, is equal to



Question for CAT Previous Year Questions: Mensuration
Try yourself:Let ABCD be a parallelogram. The lengths of the side AD and the diogonal AC are 10cm and 20cm, respectively. If the angle ∠ADC is equal to 30o then the area of the parallelogram, in sq.cm is



Question for CAT Previous Year Questions: Mensuration
Try yourself:On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two-thirds of the painted area then the perimeter of the rectangle in inches is



Question for CAT Previous Year Questions: Mensuration
Try yourself:A circle is inscribed in a thombus with diagonals 12 cm and 16 cm. The ratio of the area of circle to the area of rhombus is



Question for CAT Previous Year Questions: Mensuration
Try yourself:A solid right circular cone of height 27 cm is cut into two pieces along a plane parallel to its base at a height of 18 cm from the base. If the difference in volume of the two pieces is 225 cc, the volume, in cc, of the original cone is



Question for CAT Previous Year Questions: Mensuration
Try yourself:From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is s. Then the area of the triangle is



Question for CAT Previous Year Questions: Mensuration
Try yourself:The sum of the perimeters of an equilateral triangle and a rectangle is 90 cm. The area, T, of the triangle and the area, R, of the rectangle, both in sq cm, satisfy the relationship R = T2 . If the sides of the rectangle are in the ratio 1: 3, then the length, in cm, of the longer side of the rectangle, is



Question for CAT Previous Year Questions: Mensuration
Try yourself:Two circular tracks T1 and T2 of radii 100 m and 20 m, respectively touch at a point A. Starting from A at the same time, Ram and Rahim are walking on track T1 and track T2 at speeds 15 km/hr and 5 km/hr respectively. The number of full rounds that Ram will make before he meets Rahim again for the first time is



Question for CAT Previous Year Questions: Mensuration
Try yourself:Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to



*Answer can only contain numeric values
Question for CAT Previous Year Questions: Mensuration
Try yourself:Let C1 and C2 be concentric circles such that the diameter of C1 is 2 cm longer than that of C2. If a chord of C1 has length 6 cm and is a tangent to C2, then the diameter, in cm, of C1 is



Question for CAT Previous Year Questions: Mensuration
Try yourself:Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of 15 km/hr, 10 km/hr, and 8 km/hr, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?



*Answer can only contain numeric values
Question for CAT Previous Year Questions: Mensuration
Try yourself:In a trapezium ABCD, AB is parallel to DC, BC is perpendicular to DC and ∠BAD = 45° . If DC = 5 cm , BC= 4 cm, the area of the trapezium in sq cm is



Question for CAT Previous Year Questions: Mensuration
Try yourself:If the rectangular faces of a brick have their diagonals in the ratio 3 : 2 √3 : √15, then the ratio of the length of the shortest edge of the brick to that of its longest edge is



Question for CAT Previous Year Questions: Mensuration
Try yourself:Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is



Question for CAT Previous Year Questions: Mensuration
Try yourself:The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length of each side being 20 cm. The vertical height of the pyramid, in cm, is



Question for CAT Previous Year Questions: Mensuration
Try yourself:A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 351 cc of copper to make a number of solid right circular cylinders of each type of metal. These cylinders have the same volume and each of these has radius 3 cm. If the total number of cylinders is to be kept at a minimum, then the total surface area of all these cylinders, in sq cm, is



*Answer can only contain numeric values
Question for CAT Previous Year Questions: Mensuration
Try yourself:A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With π = 22/7, the volume, in cubic ft, of the remaining part of the cone is:

[TITA 2018]

Question for CAT Previous Year Questions: Mensuration
Try yourself:In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm, respectively. Let P be a point on CD such that AP is perpendicular to CD. Then the area, in sq cm, of triangle APD is



Question for CAT Previous Year Questions: Mensuration
Try yourself:From a rectangle ABCD of area 768 sq cm, a semicircular part with diameter AB and area 72π sq cm is removed. The perimeter of the leftover portion, in cm, is



Question for CAT Previous Year Questions: Mensuration
Try yourself:The area of a rectangle and the square of its perimeter are in the ratio 1 : 25. Then the lengths of the shorter and longer sides of the rectangle are in the ratio



Question for CAT Previous Year Questions: Mensuration
Try yourself:A parallelogram ABCD has area 48 sqcm. If the length of CD is 8 cm and that of AD is s cm, then which one of the following is necessarily true?



Question for CAT Previous Year Questions: Mensuration
Try yourself:A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8: 27: 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to:



*Answer can only contain numeric values
Question for CAT Previous Year Questions: Mensuration
Try yourself:A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is 9 π cm3. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is:

(TITA 2017)

The document CAT Previous Year Questions: Mensuration - Notes | Study Quantitative Aptitude (Quant) - CAT is a part of the CAT Course Quantitative Aptitude (Quant).
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