Previous Year XAT Questions for Geometry

1. XAT 2024 QADI | Geometry - Mensuration XAT Question

A farmer has a triangular plot of land. One side of the plot, henceforth called the base, is 300 feet long and the other two sides are equal. The perpendicular distance, from the corner of the plot, where the two equal sides meet, to the base, is 200 feet. To counter the adverse effect of climate change, the farmer wants to dig a circular pond. He plans that half of the circular area will be inside the triangular plot and the other half will be outside, which he will purchase at the market rate from his neighbour. The diameter of the circular plot is entirely contained in the base and the circumference of the pond touches the two equal sides of the triangle from inside.

If the market rate per square feet of land is Rs. 1400, how much does the farmer must pay to buy the land from his neighbour for the pond? (Choose the closest option.)

(a)
Rs. 3,16,80,000
(b)
Rs. 4,25,60,000
(c)
Rs. 6,33,60,000
(d)
Rs. 7,42,80,000
(e)
Rs. 2,98,20,000

2. XAT 2023 QADI | Geometry - Mensuration XAT Question

A non-flying ant wants to travel from the bottom corner to the diagonally opposite top corner of a cubical room. The side of the room is 2 meters. What will be the minimum distance that the ant needs to travel?

(a)
6 meters
(b)
(2√2 + 2) meters
(c)
2√3 meters
(d)
2√6 meters
(e)
2√5 meters

Answer: Option E

Video Explanation

Text Explanation :

In a 2D plane, minimum distance between 2 points is the straight line joining these points.

We can convert the cubical room in a 2D plane as shown in the figure.

∴ Shortest route from A to F = $\sqrt{4^{2} + 2^{2}}$ = 2√5.

Hence, option (e).

3. XAT 2020 QADI | Geometry - Mensuration XAT Question

A rectangular swimming pool is 50 meters long and 25 meters wide. Its depth is always the same along its width but linearly increases along its length from 1 meter at one end to 4 meters at the other end. How much water (in cubic meters) is needed to completely fill the pool?

(a)
3750
(b)
2500
(c)
1250
(d)
1874
(e)
3125

4. XAT 2020 QADI | Geometry - Mensuration XAT Question

Six drums are used to store water. Five drums are of equal capacity, while the sixth drum has double the capacity of each of these five drums. On one morning, three drums are found half full, two are found two-thirds full and one is found completely full. It is attempted to transfer all the water to the smaller drums. How many smaller drums are adequate to store the water?

(a)
Four but not three
(b)
Three or four, depending on which drum had how much water initially
(c)
Five but not four
(d)
Five may be inadequate, depending on which drum had how much water initially
(e)
Three but not two

5. XAT 2019 QADI | Geometry - Mensuration XAT Question

A gold ingot in the shape of a cylinder is melted and the resulting molten metal molded into a few identical conical ingots. If the height of each cone is half the height of the original cylinder and the area of the circular base of each cone is one ﬁfth that of the circular base of the cylinder, then how many conical ingots can be made?

(a)
40
(b)
30
(c)
60
(d)
20
(e)
10

6. XAT 2018 QADI | Geometry - Mensuration XAT Question

It takes 2 liters to paint the surface of a solid sphere. If this solid sphere is sliced into 4 identical pieces, how many liters will be required to paint all the surfaces of these 4 pieces.

(a)
2.2 liters
(b)
2.5 liters
(c)
3 liters
(d)
4 liters
(e)
None of the above

7. XAT 2018 QADI | Geometry - Mensuration XAT Question

A cone of radius 4 cm with a slant height of 12 cm was sliced horizontally, resulting into a smaller cone (upper portion) and a frustum (lower portion). If the ratio of the curved surface area of the upper smaller cone and the lower frustum is 1:2, what will be the slant height of the frustum?

(a)
12 - √3
(b)
12 - 2√3
(c)
12 - 3√3
(d)
12 - 4√3
(e)
None of the above

8. XAT 2017 QADI | Geometry - Mensuration XAT Question

The Volume of a pyramid with a square base is 200 cubic cm. The height of the pyramid is 13 cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?

(a)
12 cm
(b)
13 cm
(c)
14 cm
(d)
15 cm
(e)
16 cm

9. XAT 2017 QADI | Geometry - Mensuration XAT Question

ABCD is a rectangle. P, Q and R are the midpoint of BC, CD and DA. The point S lies on the line QR in such a way that SR: QS = 1:3. The ratio of the area of triangle APS to area of rectangle ABCD is

(a)
36/128
(b)
39/128
(c)
44/128
(d)
48/128
(e)
64/128

Answer: Option A

Text Explanation :

Let the length of the rectangle be ‘l’ and breadth be ‘b’.

The given figure is.

Let us draw a line MS parallel to DC

∆RMS ~ ∆RDQ

∴ RM : MD = RS : SQ = 1 : 3

Let the length of the rectangle (i.e., AB = CD) ABCD be 8l and width be 8b (i.e., AD = BC).

∴ AR = 4b and RM = b

Also, MS = l and SL = 7l.

Also, PL : LC = 1 : 3 [∵ RS : SQ = 1 : 3]

Area (∆ARS) = ½ × AR × SM = 2lb

Area (∆RDQ) = ½ × RD × DQ = 8lb

Area (∆ABP) = ½ × AB × BP = 16lb

Area (PSQC) = Area (∆PSL) + Area(∆SLQC)
= ½ × SL × PL + ½ × (SL + QC) × LC
= 3.5lb + 16.5lb
= 20lb

Area of ∆ASP = Area of rectangle ABCD – [Area (∆ARS) + Area (∆RDQ) + Area (∆ABP) + Area (PSQC)]
= 64lb – [2lb + 8lb + 16lb + 20lb]
= 64lb - 46lb = 18lb

∴ $\frac{A r e a (∆ A S P)}{A r e a (A B C D)}$ = $\frac{18 l b}{64 l b}$ = $\frac{36}{128}$

Hence, option (a).

10. XAT 2016 QADI | Geometry - Mensuration XAT Question

Akhtar plans to cover a rectangular floor of dimensions 9.5 meters and 11.5 meters using tiles. Two types of square shaped tiles are available in the market. A tile with side 1 meter costs Rs. 100 and a tile with side 0.5 meters costs Rs. 30. The tiles can be cut if required. What will be the minimum cost of covering the entire floor with tiles?

(a)
10930
(b)
10900
(c)
11000
(d)
10950
(e)
10430

11. XAT 2016 QADI | Geometry - Mensuration XAT Question

A square piece of paper is folded three times along its diagonal to get an isosceles triangle whose equal sides are 10 cm. What is the area of the unfolder original piece of paper?

(a)
400 sq.cm.
(b)
800 sq.cm.
(c)
800√2 sq.cm.
(d)
1600 sq.cm.
(e)
Insufficient data to answer

12. XAT 2015 QA | Geometry - Mensuration XAT Question

The figure below has been obtained by folding a rectangle. The total area of the figure (as visible) is 144 square meters. Had the rectangle not been folded, the current overlapping part would have been a square. What would have been the total area of the original unfolded rectangle?

(a)
128 square meters
(b)
154 square meters
(c)
162 square meters
(d)
172 square meters
(e)
None of the above

Answer: Option C

Video Explanation

Text Explanation :

Had the rectangle not been folded, the overlapping part would have been a square of side 6.

While unfolding, the increase in area

= Area of the triangle = $\frac{1}{2} \times 6 \times 6 = 18$

Area of the given figure = 144 square meters
∴ Area of unfolded rectangle = 144 + 18 = 162 square meters
Hence, option (c).

13. XAT 2015 QA | Geometry - Mensuration XAT Question

A solid metal cylinder of 10 cm height and 14 cm diameter is melted and re-cast into two cones in the proportion of 3 : 4 (volume), keeping the height 10 cm. What would be the percentage change in the flat surface area before and after?

(a)
9%
(b)
16%
(c)
25%
(d)
50%
(e)
None of the above

14. XAT 2015 QA | Geometry - Mensuration XAT Question

A circular road is constructed outside a square field. The perimeter of the square field is 200 ft. If the width of the road is 7√2 ft. and cost of construction is Rs. 100 per sq. ft. Find the lowest possible cost to construct 50% of the total road.

(a)
Rs. 70,400
(b)
Rs. 125,400
(c)
Rs. 140,800
(d)
Rs. 235,400
(e)
None of the above

Answer: Option B

Video Explanation

Text Explanation :

Radius of inner circle = ½ × diagonal of the square = 25√2 cm
Radius of outer circle = Radius of inner circle + width of the road = 32 cm
50% of the area of the road

$= \frac{1}{2} \times π \times [{(32 \sqrt{2})}^{2} - {(25 \sqrt{2})}^{2}]$

= 1254 cm²

Cost = 1254 ×100 = Rs. 125,400

Hence, option (b).

15. XAT 2012 QA | Geometry - Mensuration XAT Question

Ram, a farmer, managed to grow shaped-watermelons inside glass cases of different shapes. The shapes he used were: a perfect cube, hemi-spherical, cuboid, cylindrical along with the normal spherical shaped watermelons. Thickness of the skin was same for all the shapes. Each of the glass cases was so designed that the total volume and the weight of the all the water-melons would be equal irrespective of the shape.

A customer wants to but water-melons for making juice, for which the skin of the water-melon has to be peeled off, and therefore is a waste. Which shape should the customer buy?

(a)
Cube
(b)
Hemi-sphere
(c)
Cuboid
(d)
Cylinder
(e)
Normal spherical

16. XAT 2012 QA | Geometry - Mensuration XAT Question

A spherical metal of radius 10 cm is molten and made into 1000 smaller spheres of equal sizes. In this process the surface area of the metal is increased by:

(a)
1000 times
(b)
100 times
(c)
10 times
(d)
No change
(e)
None of the above

17. XAT 2012 QA | Geometry - Mensuration XAT Question

Suresh, who runs a bakery, uses a conical shaped equipment to write decorative labels (e.g., Happy Birthday etc.) using cream. The height of this equipment is 7 cm and the diameter of the base is 5 mm. A full charge of the equipment will write 330 words on an average. How many words can be written using three fifth of a litre of cream?

(a)
45090
(b)
45100
(c)
46000
(d)
43200
(e)
None of the above

18. XAT 2012 QA | Geometry - Mensuration XAT Question

Carpenter Rajesh has a circular piece of plywood of diameter 30 feet. He has cut out two disks of diameter 20 feet and 10 feet. What is the diameter of the largest disk that can be cut out from the remaining portion of the plywood piece?

(a)
>8.00 feet and ≤ 8.20 feet
(b)
> 8.21 feet and ≤ 8.40 feet
(c)
> 8.41 feet and ≤ 8.60 feet
(d)
> 8.61 feet and ≤ 8.80 feet
(e)
> 8.81 feet and ≤ 9.00 feet

19. XAT 2012 QA | Geometry - Mensuration XAT Question

A property dealer bought a rectangular piece of land at Rs. 1000/sq. ft. The length of the plot is less than twice its breadth. Due to its size, there were no buyers for the full plot. Hence he decided to sell it in smaller sized pieces as given below.

The largest square from one end was sold at Rs. 1200/sq. ft. From the remaining rectangle the largest square was sold at Rs. 1150/sq. ft.

Due to crash in the property prices, the dealer found it difficult to make profit from the sale of the remaining part of the land. If the ratio of the perimeter of the remaining land to the perimeter of the original land is 3 : 8, at what price (in Rs.) the remaining part of the land is to be sold such that the dealer makes an overall profit of 10%?

(a)
500/sq. ft.
(b)
550/sq. ft.
(c)
600/sq. ft.
(d)
650/sq. ft.
(e)
None of the above.

Geometry - Mensuration - Previous Year CAT/MBA Questions

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