Consider a cylinder of height h cm and radius <span id="MathJax-Element-66-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).

What is the vertical spacing between the two consecutive turns?

The area of an equilateral triangle of side 8 cm is

Find the circumference of a circular disk whose area is 100 π square centimeters

In the diagram, PQR and RST are two semicircles with diameters 7 cm and 3.5 cm respectively and PT = 3.5 cm respectively and PT = 3.5 cm.



What is the area of the region PQRST enclosed by the figure, to the nearest whole number

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 rectangular pool 20 m wide and 60 m long is surrounded by a walkway of uniform width. If the total area of the walkway is 516m^2,how wide, in metres, is the walkway?

A cone of height 12 cm has a volume of 330 cm³.
The volume of a cone wih the same radius but of height 8cm is

In the figure, PQ//TS, TP//SQ, PQ = 4 cm, QR = 3 cm and RS = 6 cm. The ratio of the area of PQST to the area of PQRST is

Rectangular tiles each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110 cm by 130 cm, such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is

The material within a hollow sphere of internal and external diameters 4 cm and 8 cm respectively, is melted and cast into the form of a right circular cone of base diameter 8 cm. Find the height of the cone.

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

Water flows at the rate of 10 metres/minute from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cms and depth 24 cms?

The length of the circumference of a circle equals the perimeter of a triangle of equal sides, and also the perimeter of a square. The areas covered by the circle, triangle, and square are c, t and s, respectively. Then,

A open cylindrical container has a base radius of 3.5 cm.
If the ratio of the area of its base to that of its curved surface is 1 : 6,
the height of the container is

The surface area of a sphere of radius 3.5 cm is
take (π = 22/7)

A storage tank in the shape of a cuboid of base 2.5 m by 2m can hold up to 7,500 litres of water.
The height of the tank 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,
the total volume of wood in the box is

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 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

Let ABCDEF be a regular hexagon. What is the ratio of the area of the <span id="MathJax-Element-93-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="ΔACE">ΔACEΔACE to that of the hexagon ABCDEF?

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.

Find the area of the shaded region.

An arc of a circle of radius 5.6 cm subtends an angle of 45° at the center of the circle. If π = 22/7,
the length of the arc is

PQRS is a parallelogram and ST is perpendicular to QR. If the area of triangle PSR  is 25 cm² and|PS| = 10 cm, the length ST is