An equilateral triangle circumscribes all the six circles, each with radius 1 cm. What is the perimeter of the equilateral triangle?

A right circular cone has a radius of 5 cm and a vertical angle of 60°.
The height of the cone is

A square tile measures 20 cm by 20 cm.
How many of such tiles will cover a floor measuring 5m by 4m

A circular hall, surmounted by a hemispherical roof, contains 5236<span id="MathJax-Element-50-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="m3">m3m3 of air and the internal diameter of the room is equal to the height of the highest point of the roof above the ground. Find the height of the room (Take <span id="MathJax-Element-51-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="π=3.1416)">π=3.1416)π=3.1416) .

In a bullet the gun powder is to be filled up inside the metallic enclosure. The metallic enclosure is made up of a cylindrical base and conical top with the base of radius 5 cm. The ratio of height of cylinder and cone is 3 : 2. A cylindrical hole is drilled through the metal solid with height two-third the height of metal solid. What should be the radius of the hole, so that the volume of the hole (in which gun powder is to be filled up) is one-third the volume of metal solid after drilling?

The ratio of the sides of two similar rectangular blocks is 5 : 3.
If the volume of the smaller block is 324 cm³,
that of the other block is

The area of the trapezium PQRS in the figure is

A rectangular sheet of paper, when halved by folding it at the mid point of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle?

Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be k% lower than the volume of B. The value of k must be

The two parallel sides of a trapezium are 4 cm and 8 cm and are separated by a distance of 5 cm.
The area of the trapezium is

A sector of a circle of radius 14 cm which subtends an angle of 120° at the center is bent to form a cone.
The base radius of the cone is

One of the two parallel sides of a trapezium is one-half the length of the other.
If the height of the trapezium is 7 cm and its area is 52.5 cm²,
the length of the parallel sides are

There is a vast grassy farm in which there is a rectangular building of the farmhouse whose length and breadth is 50 m and 40 m respectively. A horse is tethered at a corner of the house with a tether of 80 m long. What is the maximum area that the horse can graze?

P, Q, S and R are points on the circumference of a circle of radius r, such that PQR is an equilateral triangle and PS is a diameter of the circle. What is the perimeter of the quadrilateral PQSR?

A parallelogram of area 425 cm² has a height of 17cm.
The length of the base is

An open, rectangular wooden box of internal depth 40 cm has a base of internal dimensions 50 cm by 30 cm.
If the box is made of wood of thickness 1 cm,
find the cost to the nearest dollar of painting the box if it costs $100 to paint one square meter

Glass spheres (which submerge fully in water) of radius 7 mm are dropped into a cylindrical vessel containing some water. The diameter of the vessel is 14 cm. Find how many spheres have been dropped in it if the water level rises by 3.5 cm?

Consider a cylinder of height h cm and radius <span id="MathJax-Element-75-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="r=2π">r=2πr=2π cm as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindrical surface, starting at point A and ending at point B, gives a maximum of n turns (in other words, the string’s length is the minimum length required to wind n turns).

In the set-up of the previous two questions, how is h related to n

A farmer has decided to build a wire fence along one straight side of his property. For this, he planned to place several fence-posts at 6 m intervals, with posts fixed at both ends of the side. After he bought the posts and wire, he found that the number of posts he had bought was 5 less than required. However, he discovered that the number of posts he had bought would be just sufficient if he spaced them 8 m apart. What is the length of the side of his property and how many posts did he buy?

One of the diagonals of a rhombus is 15 cm long.
If the rhombus has an area of 60 cm²,
the length of the other diagonal is

All five faces of a regular pyramid with a square base are found to be of the same area. The height of the pyramid is 3 cm. The total area of all its surfaces is

Find the volume of a closed cylindrical container with radius 5 cm and a height of 34 cm.

Four horses are tethered at four corners of a square plot of side 14 m so that the adjacent horses can just reach one another. There is a small circular pond of area 20 m² at the centre. Find the ungrazed area.

A solid cone of metal of radius r and height h cm is melted into a cube of length a. If h + r = 10 cms, and the volume of the cube formed is maximum then the radius of the cone in cms is

A square, whose side is 2 m, has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of the octagon, in meters, is