CAT Mensuration Questions & Solutions

A sample of real CAT Mensuration past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 17 Mensuration questions in all — sign up free to practise them timed.

1. Q1.CAT 2024

   The surface area of a closed rectangular box, which is inscribed in a sphere, is 846 sq cm, and the sum of the lengths of all its edges is 144 cm. The volume, in cubic cm, of the sphere is

   • 1125 $\pi$

   • 750 $\pi$

   • 1125 $\pi \sqrt{2}$

   • 750 $\pi \sqrt{2}$

2. Q2.CAT 2023

   A rectangle with the largest possible area is drawn inside a semicircle of radius 2 cm. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is

   • 2 : 1

   • 1 : 1

   • $\sqrt{5} : 1$

   • $\sqrt{2} : 1$

3. Q3.CAT 2023

   In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is

   Answer: 54

4. Q4.CAT 2023

   In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the figures ABP, APQ, and AQCD are in geometric progression. If the area of the figure AQCD is four times the area of triangle ABP, then BP : PQ : QC is

   • 1:2:4

   • 1:2:1

   • 2:4:1

   • 1:1:2

5. Q5.CAT 2022

   A trapezium $ABCD$ has side $AD$ parallel to $BC, \angle BAD = 90^\circ, BC = 3$ cm and $AD= 8$ cm. If the perimeter of this trapezium is 36 cm, then its area, in sq. cm, is

   Answer: 66

6. Q6.CAT 2021

   If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is

   • $4\sqrt{6}$

   • $6\sqrt{6}$

   • $\sqrt{6}$

   • $2\sqrt{6}$

7. Q7.CAT 2021

   If a rhombus has area 12 sq cm and side length 5 cm, then the length, in cm, of its longer diagonal is

   • $\sqrt{37}+\sqrt{13}$

   • $\sqrt{13}+\sqrt{12}$

   • $\frac{\sqrt{37}+\sqrt{13}}{2}$

   • $\frac{\sqrt{13}+\sqrt{12}}{2}$

8. Q8.CAT 2021

   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

   • 120000

   • 90000

   • 100000

   • 160000

9. Q9.CAT 2021

   Let ABCD be a parallelogram. The lengths of the side AD and the diagonal AC are 10cm and 20cm, respectively. If the angle $\angle ADC$ is equal to $30^{0}$ then the area of the parallelogram, in sq.cm is

   • $\frac{25(\sqrt{5}+\sqrt{15})}{2}$

   • $25(\sqrt{3}+\sqrt{15})$

   • $\frac{25(\sqrt{3}+\sqrt{15})}{2}$

   • ${25(\sqrt{5}+\sqrt{15})}$

10. Q10.CAT 2020

    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

    • 243

    • 232

    • 256

    • 264

11. Q11.CAT 2020

    A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of circle to the area of rhombus is

    • $\frac{6\pi}{25}$

    • $\frac{5\pi}{18}$

    • $\frac{3\pi}{25}$

    • $\frac{2\pi}{15}$

12. Q12.CAT 2020

    In a trapezium $ABCD$, $AB$ is parallel to $DC$, $BC$ is perpendicular to $DC$ and $\angle BAD=45^{0}$. If $DC$ = 5cm, $BC$ = 4 cm,the area of the trapezium in sq cm is

    Answer: 28

CAT Mensuration previous year questions with solutions — AthenaPrep