The CAT QA section requires speed and accuracy, along with a thorough understanding of the Mensuration. This article provides a set of MCQs on Mensuration to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT 2025 exam preparation
Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.
The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.
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CAT MCQs on Mensuration
1. A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio a:b. If the radius of the circle is r, then the area of the triangle is
A
\(\frac{2abr^2}{a^2+b^2}\)
B
\(\frac{abr^2}{a^2+b^2}\)
C
\(\frac{abr^2}{2(a^2+b^2)}\)
D
\(\frac{4abr^2}{a^2+b^2}\)
2. The area of the quadrilateral bounded by the \(Y\) -axis, the line \(x = 5\) , and the lines \(|x-y|-|x-5|=2\), is
A
45
B
55
C
60
D
None of Above
3. The area, in sq. units, enclosed by the lines \(x=2\), \(y=|x-2|+4\), the \(X\)-axis and the \(Y\)-axis is equal to
A
8
B
12
C
10
D
6
4. The vertices of a triangle are (0,0),(4,0) and (3,9). The area of the circle passing through these three points is
A
\(\frac{14π}{3}\)
B
\(\frac{12π}{5}\)
C
\(\frac{123π}{7}\)
D
\(\frac{205π}{9}\)
5. In a trapezium ABCD, AB is parallel to DC, BC is perpendicular to DC and \(∠BAD=45°\). If DC=5cm , BC=4 cm, the area of the trapezium in sq cm is ? [This Question was asked as TITA]
A
\(25 \ cm^2\)
B
\(26 \ cm^2\)
C
\(28\ cm^2\)
D
\(30\ cm^2\)
6. Two ships are approaching a port along straight routes at constant speeds. Initially,the two ships and the port formed an equilateral triangle with sides of length 24 km. When the slower ship travelled 8 km,the triangle formed by the new positions of the two ships and the port became right-angled. When the faster ship reaches the port, the distance,in km,between the other ship and the port will be
A
4
B
6
C
12
D
8
7. 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
A
\(8\sqrt{3}\)
B
12
C
\(5\sqrt{5}\)
D
\(10\sqrt{2}\)
8. 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
A
\(8464\pi\)
B
\(928\pi\)
C
\(1044(4+\pi)\)
D
\(1026(1+\pi)\)
9. Three circles with centers at ‘A’, ‘B’ and ‘C’ touches each other externally as shown in the figure. If AB = 16cm, BC = 8 cm and AC = 12 cm, then find the radii of all three circles.
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A
10 cm, 6 cm and 2 cm
B
2 cm, 5 cm and 3 cm
C
6 cm, 8 cm and 9 cm
D
12 cm, 10 cm and 5 cm
10. An isosceles triangle PQR is inscribed inside a circle. If PQ = PR = \(8\sqrt5\) cm and QR = 16 cm, then find the radius of the circle.
A
8 cm
B
12 cm
C
15 cm
D
10 cm
11. PQR is an equilateral triangle having perimeter equal to 45 metres. If ‘O’ is the centroid of the equilateral triangle PQR, then find the length of OP
A
\(5\sqrt3 \) cm
B
\(8\sqrt5 \) cm
C
\(10\sqrt3 \) cm
D
\(5\sqrt5 \) cm
12. A rectangular sheet of metal is rolled along its length to form a cylinder of volume 269500 cm3and lateral surface area 15400 cm2. If the sheet would have been cut in two halves vertically dividing its length in 2:3 ratio and then these parts are rolled into two cylinders along their lengths, then find the sum of volume of both the cylinders formed and also find the difference between area of both parts of sheet when cut.
A
140144 cm3, 3080 cm2
B
141144 cm3, 3088 cm2
C
140140 cm3, 3080 cm2
D
141141 cm3, 3800 cm2
13. A solid wooden cylindrical log of radius 35 cm and height 20 cm is used to make a glass holder box. 12 conical holes of height 15 cm and radius 3.5 cm are drilled into the upper surface of the log to accommodate glasses. The remaining upper surface area which is solid is covered with woolen cloth that costs Rs.4 per sq. cm and the inner surfaces of the holes are polished at the rate of Rs.0.25 per sq. cm. What is the total cost incurred ?
A
Rs 14047
B
Rs 15220
C
Rs 15776.5
D
Rs 16258
14. The area of a circle is equal to the sum of the area of a rectangle and a square. The length of the rectangle is 1 cm more than the twice of the side of the square and breadth of the rectangle is 1.5 cm less than \(\frac{3}{2}\) times of the radius of the circle. What is the difference between the circumference of the circle and perimeter of the square if the side of the square is 6 cm less than the radius of the circle?
A
110 cm
B
104 cm
C
103 cm
D
105 cm
15. The area of the closed region bounded by the equation \(| x | + | y | = 2\) in the two-dimensional plane is
A
\( 4\pi\)
B
4
C
8
D
\( 2\pi\)
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