XAT Mensuration MCQs with Solutions: Practice XAT Previous Year Questions (PYQs)

There are five dustbins along a circular path at different places. Ramesh takes multiple rounds of the path every morning, always at the same speed. He noticed that it took him a different number of steps to walk between any two consecutive dustbins. Ramesh also noticed that starting from any of the dustbins, it took a minimum 360 steps to reach every second dustbin, and a maximum 1260 steps to reach every third dustbin. If Ramesh's step size is 0.77 meter, and the width of the path is negligible, which of the following can be the radius of the circular path?

If the diagonals of a rhombus of side 15 cm are in the ratio 3:4, find the area of the rhombus.

Let ABC be an isosceles triangle. Suppose that the sides AB and AC are equal and let the length of AB be x cm. Let b denote the angle ∠ABC and \(sin\ b = \frac 35\). If the area of the triangle ABC is M square cm, then which of the following is true about M?

A farmer has a quadrilateral parcel of land with a perimeter of 700 feet. Two opposite angles of that parcel of land are right angles, while the remaining two are not. The farmer wants to do organic farming on that parcel of land. The cost of organic farming on that parcel of land is Rs. 400 per square foot.
Consider the following two additional pieces of information:
1. The length of one of the sides of that parcel of land is 110 feet.
2. The distance between the two corner points where the non-perpendicular sides of that parcel of land intersect is 265 feet.
To determine the amount of money the farmer needs to spend to do organic farming on the entire parcel of land, which of the above additional pieces of information are MINIMALLY SUFFICIENT?

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 unfolded original piece of paper?

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 all the watermelons would be equal irrespective of the shape. A customer wants to buy watermelons for making juice, for which the skin of the watermelon has to be peeled off, and therefore is a waste. Which shape should the customer buy?

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?

In the picture below, EFGH, ABCD are squares, and ABE, BCF, CDG, DAH are equilateral triangles. What is the ratio of the area of the square EFGH to that of ABCD?

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 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?

Adu and Amu have bought two pieces of land on the Moon from an e-store. Both the pieces of land have the same perimeters, but Adu’s piece of land is in the shape of a square, while Amu’s piece of land is in the shape of a circle. The ratio of the areas of Adu’s piece of land to Amu’s piece of land is:

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?

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?

Akhtar plans to cover a rectangular floor of dimensions $9.5$ m and $11.5$ m using tiles. Two types of square tiles are available: side $1$ m costs \rupee{100, and side $0.5$ m costs \rupee{}30. Tiles can be cut if required. What is the {minimum} cost to cover the entire floor?}

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?