Advertisements
Advertisements
प्रश्न
A well with 6 m diameter is dug. The earth taken out of it is spread uniformly all around it to a width of 2 m to form an embankment of height 2.25 m. Find the depth of the well.
उत्तर
Radius of the well (r)
= `(6)/(2)`
= 3m
Volume of earth dug out of the well
= πr2h ...(Volume of cylinder)
= π x (3)2 x h
= 9πh m2
Area of embankment = πR2 - πr2
Where R = r + width of the embankment
= 3 + 2
R = 5m
Area of embankment
= π52 -π32
= 16π m2
Volume of earth dug out for the embankment
= area of embankment x height
9πh = 16π x 2.25
h = `(16π xx 2.25)/(9π)`
∴ h = 4m
∴ The depth of the well is 4m.
APPEARS IN
संबंधित प्रश्न
A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs.12.50 per m2.
`["Assume "pi=22/7]`
The diameter of the base of a right circular cylinder is 42 cm and its height is 10 cm. Find the volume of the cylinder.
A piece of ductile metal is in the form of a cylinder of diameter 1 cm and length 5 cm. It is drawnout into a wire of diameter 1 mm. What will be the length of the wire so formed?
Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cylindrical tank, the radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes?
A cylindrical tube, open at both ends, is made of metal. The internal diameter of the tube is 10.4 cm and its length is 25 cm. The thickness of the metal is 8 mm everywhere. Calculate the volume of the metal.
Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cylindrical tank. The radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes?
A road roller is cylindrical in shape, its circular end has a diameter of 1.4 m and its width is 4 m. It is used to level a play ground measuring 70 m × 40 m. Find the minimum number of complete revolutions that the roller must take in order to cover the entire ground once.
A hollow garden roller, 1 m wide with outside diameter of 30 cm, is made of 2 cm thick iron. Find the volume of the iron. If the roller rolls without sliding for 6 seconds at the rate of 8 complete rounds per second, find the distance travelled and the area covered by the roller in 6 seconds.
The radius and height of a cylinder are in the ratio 5:7 and its curved surface area is 5500 sq.cm. Find its radius and height.
Two cylinders with equal volume will always have equal surface areas.
