Geometry PYQ — Page 4

From the top of a building 78 m high, the angles of depression of the bottom and the top of a tower are observed to be 45° and 30° respectively. Determine the approximate height of the tower so observed?

If a metallic rod of 10 cm length and 2 cm radius is stretched into a wire of 40 m length having uniform thickness, then find the radius of the stretched wire.

The distance between points A (-5, 7) and B (-1, 3) is:

Four circles of equal radius are drawn with centers, A, B, C and D such that ABCD is a square of side 14 cm and the circles touch externally as in the figure. The area of the shaded region bounded by the 4 circles is: (Take $\pi = \frac{22}{7}$) 

The angles of elevation of the top of a tower from two points at a distance of 5 meters and 20 meters along the same straight line from the base of the tower, are complementary. Find the height of the tower.

The base diameter of a cylinder is 21 cm and the height is 28 cm, then: (A) Radius of cylinder = 10.5 cm (B) Volume = 12936 cm³ (C) Curved Surface Area = 1848 cm² (D) Total surface area = 2541 cm² Which of the following is/ are correct? Choose the correct answer from the options given below:

Find the value of x in the adjoining figure, if it is given that PR and QS are diameters of the circle. 

What will be the reflection of point (2, 3) in the second quadrant?

A 2 m tall boy is 30 m away from a tower. The angle of elevation of the top of the tower from his eye is 45°. What is the height of the tower?

If the length of a cuboid is increased by 20% and its breadth is decreased by 20%, then the volume of cuboid

The ratio of the radius and height of a cone is 3:4. Its volume is $37\frac{5}{7}$ cm³. The slant height of the cone is

The shadow of the pole standing on a level surface is found to be 5 m shorter when the sun's elevation is 60° than when it is 45°. What is the height of the pole?

In the adjoining figure, a rectangle has dimensions of 18 cm x 12 cm. The area of the parallelogram (shaded portion) is 

A solid sphere of radius 15 cm is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 9 cm and its height is 100 cm, find the uniform thickness of the cylinder.

If the points A(3, 0), B(x, 5), C(-1, 4) and D(-2, -1) are the vertices of a rhombus, taken in order, find the value of x.

A flask in the shape of a right circular cone of height 36 cm is completely filled with tea. The tea is then poured into another right circular cylindrical flask whose radius is two-third of the radius of base of the circular cone. Then, the height of the tea in the cylindrical flask is

From the top of a tower, the angles of depression of two objects A and B (situated on the ground on the same side of the tower) are observed to be 30° and 60°, respectively. If the distance between the objects is 200√3 m, then the height of the tower is?

If the ratio of the radii of the sphere and hemisphere is √3:2, then determine the ratio of their total surface area?

If the distance between the points (2, -2) and (5, k) is 5 units, then one of the possible values of k shall be which of the following?

A solid, metallic right circular cone of radius 7 cm and height 3 cm is melted into three cubes. If the sides of two cubes are 3 cm and 5 cm, then the side of the third cube will be how much?

The angle of elevation of the top of a tower from a certain point is 60°. If the observer moves 10 m away from the tower, the angle of elevation of the top of the tower decreases by 15°. The height of the tower is:

The area of the right-angled isosceles triangle having hypotenuse A cm is:

If two tangents inclined at an angle 60° are drawn to a circle of radius 5 cm, then what is the length of each tangent?

If a cone and sphere have equal radii and volumes, then determine the ratio of the diameter of the sphere to the height of the cone?