One side of an equilateral triangle is 36 cm. The mid points of its sides are joined to form another triangle whose mid-points are in turn joined to form still smaller triangle. This process continues indefinitely. Find the sum of the perimeters of all the triangles.

A metallic wire of length 3 km and thickness 4 mm is recasted to form a cube. The area of each face of cube is same as area of a circle. What will be the radius of the circle?(in cm) (Use π = 3.14)

The capacities of two hemispherical vessels are 6.4 litres and 21.6 litres. The ratio of their inner radii is

If A1, A2 and A3 be the total surface area of a right circular cone, a sphere and a right circular cylinder, all have equal radii and equal heights, and also, the radius is equal to the height, then A1 : A2 : A3 = ?

Find the altitude of a rhombus whose area is 45 cm2 and perimeter 180 cm.

If the perimeters of a rectangle and a square are equal, and it is known that the length is twice the breadth in the rectangle, find the ratio of the length of the rectangle and side of the square is

A solid iron sphere of diameter 6 cm is melted and made into a hollow cylindrical pipe of external diameter 10 cm and of length 4 cm. The thickness of the pipe is:

The length of a rectangular room is twice of its breadth. The cost of flooring is Rs. 100 per square meter and the total cost involved is Rs. 5000. Find the length of the room.

The ratio of the heights of two triangles is 4 ∶ 3 and the ratio of their areas is 6 ∶ 7. What is the ratio of their bases?

The area (in m2) of the square which has the same perimeter as a rectangle whose length is 56 m and is 4 times its breadth is:

How many balls of radius 2 cm can be made by melting a bigger ball of diameter 16 cm? (Take π = 22/7)

A path of 2.5 m width surrounds a rectangular garden of length 10 and breadth 8 m. Area of the garden, inclusive of the path is

If the difference between an exterior angle of a regular polygon of n side and an exterior angle of another regular polygon of (n + 1) sides is equal to 5°, then the value of n is

If a circular (spherical) marble of 10 cm radius has been molten to form smaller circular marbles of 0.5 cm. radius, then how many smaller marbles will be formed?

A wire when bent in the form of a square encloses an area of 484 sq.cm. What will be the enclosed area when the same wire is bent into the form of a circle? (Take \(\pi = \frac{{22}}{7}\))

A cylindrical vessel of radius 7 cm contains water. A solid hemisphere of radius 6 cm is dipped into the water until it is completely immersed. The water level in the vessel will rise by

20 Buckets of water fill a tank when the capacity of each bucket is 18 litres. How many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres?

The volume (in m3) of rain water that can be collected from 1.4 hectares of ground in a rainfall of 4 cm is?

For a cone, the radius is 6cm and the height is 12 cm. What is the volume of the cone?

ABCD is a trapezium, such that AB = CD and AD|| BC. AD = 5 cm, BC = 9 cm. If area of ABCD is 35 sq.cm, then CD is:

A square of side 22 cm is made from a single wire. The same wire is then bent to form a circle. The area of the circle formed is (π = 22/7)

The difference between the length and breadth of a rectangle is 21 m. If its perimeter is 250 m, then its area is:

The length of one leg of a right-angled isosceles triangle is 6 cm. what is its area?

The radii of a sphere and a right circular cylinder are equal and their curved surface areas are also equal. Then the ratio of their volumes is

The perimeter of a square is equal to the circumference of a circle. What is the ratio between the side of the square and the radius of the circle?

The area and length of a rectangle are 144 m2 and 9 m respectively. Its diagonal will be

ABCD is a parallelogram. P, Q are the midpoints of sides BC and CD respectively. If the area of Δ ABC is 24 cm2, then the area of Δ APQ is

If the volume of a sphere is numerically equal to its surface area then its diameter is:

ABC is a triangle with sides AC = 20 cm, AB = 12 cm and BC = 16 cm. E, F and G are the mid-points of the triangle ABC. Find the perimeter of the triangle formed by joining the mid-points.

The radius of a wire is decreased to one-third. If volume remains the same, length will increase by :