CMAT Geometry questions

What is the area of an equilateral triangle whose inscribed circle has radius R?

In the following diagram, if the shaded area is one half the area of triangle ABC and angle ABC is right angle then the length of line segment AD is

The least number of square tiles required to pave the floor of a room 15 m 91 cm and 9 m 46 cm broad is

If a 30 meter ladder is placed against a wall such that it just reaches the top of the wall, if the horizontal distance between the wall and the base of the ladder is 1/3rd of the length of ladder, then the height of wall is :

A copper wire having length of 243m and diameter 4 mm was melted to form a sphere. Find the diameter of the sphere :

In triangle PQR. PS is perpendicular to QR and S divides QR in the ratio of 3 : 1 internally. If PQ=21 and PR =9,find QR.

A roller is 4m long and has a diameter of 0.7m. It takes exactly 2000 rotations of the roller to level a road. If the cost of using the roller is Rs.4 per square metres, then the total cost of levelling the roadis :
Assume, $$\pi=\frac{22}{7}$$

In a $$\triangle ABC,D,E$$ and $$F$$ are the mid-points of the sides AB, BC and CA respectively. Then the ratio of the area of a $$\triangle DEF$$ and the area of a $$\triangle ABC$$ is:

Which of the following sets of numbers can be used as the lengths of the sides of a triangle ?

What is the farthest distance between two points on a cylinder of: HEIGHT 8 and RADIUS 8 ?

In a triangle ABC, AD is the bisector of angle A. If AC =4.2 cm, DC = 6 cm, BC =10 cm, find AB.

The maximum value of 3 $$cosx+4 sinx+8$$ is

The length, breadth and height of a rectangular cuboid are in the ratio 1: 2 : 3. If the length, breadth and height are increased by 100% each then what would be the increase in the volume of the cuboid ?

It costs Rs. 6000/- and Rs. 6,100- respectively to paint the 4 walls of 2 square halls, of the same height. If the length of one hall exceeds the length of the other by 1 m and the cost of painting is Rs. 5 per sq.m., what is the height of the two walls ?

A rectangular box of width(a), length(b), and height(c) has a solid cylinder of height 'c' and of diameter 'a' placed within it. If a= 6, b =8 and c =10, how much volume is left in the rectangular box ?

Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed.

In a building there are 30 cylindrical pillars. The radius of each pillar is 35 cm and height is 5 m. Find out the cost of painting the curved surface of half the number of pillars. The rate of painting is Rs. 10 per $$m^2$$.

How many iron balls, each of radius 1 cm, can be made from a sphere whose radius is 8 cm?

In a circle of radius 6 cm, arc AB makes an angle of 114° with centre of the circle O.
What is angle ABO?

In the figure, PQ is a diameter of the circle. Angle PQS = $$35^\circ$$. Find angle QRS.