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An iron pipe 20 cm long has exterior diameter equal to 25 cm. If the thickness of the pipe is 1 cm, find the whole surface area of the pipe.
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A canal 3 m wide and 1m 20 cm deep. The water in the canal is flowing with speed of 20 km/hr. How much area will it irrigate in 20 minutes if 8 cm of standing water is desired?
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Volume of water that flows in one hour
In 20 minutes the volume of water flows
Area irrigate
The interior of a building is in the form of a cylinder of diameter 4.3 m and height 3.8 m surmounted by cone whose vertical angle is 90Â°. Find the surface area of the interior of the building.
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Volume of building
Surface of building
A cone of radius 4 cm is divided into two parts by drawing a plane through the midpoint of its axis and parallel to its base. Compare the volumes of the two parts.
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Height of small cone
Radius
Volume
Volume of cone
Volume of frustum
Ratio
Find the number of metallic circular disc with 1.5 cm base diameter and of height 0.2 cm to be metled to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
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Radius,
Height,
If the radius of base of a right circular cylinder is halved, keeping the height same, what is the ratio of the volume of the reduced cylinder to that of the original?
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New radius
New volume
Ratio
How many metres of cloth 1 m 10 cm wide will be required to make a conical circus tent whose height is 12 m and the radius of whose base is 10 m? Also, find the cost of cloth at Rs. 7 per m.
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Cost
Three cubes of iron whose edges are in the ratio 3 : 4 : 5 are melted and converted into a single cube whose diagonal is \(12\sqrt3\ cm \). Find the edges of the three cubes.
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Let sides be
A/Q
Edge of the three cubes respectively
A metallic toy in the form of a cone of radius 11 cm and height 62 cm mounted on a hemisphere of the same radius is melted and recast into a solid cube. Find the surface area of the cube thus formed.
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Volume of hemisphere + volume of cone = volume of cube
A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm respectively. Find the height of the bucket.
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Volume litres
volume
A wall \(24\ m \) long, \(0.4\ m \) thick and \(6\ m \) high is constructed with the bricks each of dimensions \(25\ cm \times 16\ cm \times 10\ cm\). If the mortar occupies \(\dfrac{1}{10} \)th of the volume of the wall, then find the number of bricks used in constructing the wall.
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Volume of wall
Volume of mortar
Volume of bricks
volume of one brick
Np. of bricks
The circumference of the base of a 9 m high wooden solid cone is 44 m. Find the volume of the cone.
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Volume
A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones each of diameter 7 cm and height 3 cm. Find the number of cones so formed.
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Volume of sphere
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder of same radius. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
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Inner surface area
A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.
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Earth dug out
Volume of cuboid
A well with 7 m inside diameter is dug 22 m deep, earth taken out of it has been spread all round it to a width of 10.5 m to form an embankment. Find the height of hte embankment so formed.
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Volume of earth
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest \(cm^2.\ \left(\pi=\dfrac{22}{7}\right) \)
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Right circular cylinder having diameter 12 cm and height 15 cm is full of iceâ€“cream. This iceâ€“cream is to be filled in cones of height 12 cm and diameter 6 cm having a hemispherical shape on the top. Find the number of such cones which can be filled with iceâ€“cream
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Volume of cylinder
Volume of cone
Volume of hemisphere
No. of cones
The rain water from a roof \(22\ m \times 20\ m\) drains into a conical vessel having the diameter of base as \(2\ m \) and height \(3.5\ m \). If the vessel is just full, find the rainfall in mm.
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Volume of water
Volume of cylindrical vessel
An open container made up of a metal sheet is in the form of a frustum of a cone of height 8 cm with radii of its lower and upper ends as 4 cm and 10 cm respectively. Find the cost of the metal used, if it costs Rs 5 per 100 \( cm^2\) (Use \(\pi=3.14 \)).
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TSA of frustum
Cost of metal used
Solid shperes of diameter 6 cm each are dropped into a cylindrical beaker containing some water and are fully submerged. The water in the beaker rises by 40 cm. Find the number of soild spheres dropped into the beaker if the diameter of the beaker is 18 cm.
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Radius of sphere
Volume of sphere
Volume of rise in water
A/Q
Water is flowing at the rate of 5 km/hour through a pipe of diameter 14 cm into a rectangular tank, which is 50 m long and 44 m wide. Determine the time in which the level of water in the tank will rise by 7 cm.
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volume of water flowing through the cylindrical pipe in x hours
volume of water that falls into the tank
A/Q
A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
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Greatest diameter
Radius
Surface area
Surface area of base of hemisphere
An ice cream cone consisting of a cone is surmounted by a hemisphere. The common radius of hemisphere and cone is 3.5 cm and the total height of icecream cone is 12.5 cm. Calcualte the volume of icecream in the cone.
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V of ice cream
A semicircular sheet of paper of diameter 28 cm is bent into an open conical cup. Find the depth and capacity of the cup.
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Capacity of the cup
50 circular plates, each of radius 7 cm and thickness 0.5 cm, are placed one above another to form a solid right circular cylinder. Find the total surface area and the volume of the cylinder so formed.
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Radius of plate
Height of cylinder
Surface area
A rectangular sheet of paper \(44\ cm \times 18\ cm\) is rolled along its length \((44\ cm)\) and a cylinder is formed. Find the volume of the cylinder.
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Volume
A toy is in the form of a cone mounted on a hemisphere of same radius 3.5 cm and total height of the toy is 15.5 cm, find the total surface area and the volume of the toy.
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TSA of toy = CSA of toy + CSA of hemisphere
A solid sphere of diameter 14 cm is cut into two halves by a plane passing through the centre. Find the combined surface area of the two hemispheres so formed.
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Surface area of one hemisphere
Surface area of two hemisphere
The internal and external radii of a hollow spherical shell are 3 cm and 5 cm respectively. If it is melted to form a solid cylinder of height \(10\dfrac{2}{3} \) cm, find the diameter of the cylinder.
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Volume of hollow sphere
volume of cylinder
A/Q
Diameter
A cylindrical copper rod of diameter 1 cm and length 8 cm is drawn into a cylindrical wire of length 18 m and of uniform thickness. Find the thickness of the wire.
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Volume of rod
Length of new wire
diameter
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/ hr, in how much time will the tank be filled?
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Inner radius
Rate of flow of water = 3000 m/h
Volume of water speed time
volume of the tank
A/Q
A sphere of radius 6 cm is dropped into a cylindrical vessel party filled with water. The radius of the vessel is 8 cm. If the sphere is submerged completely, then find the increase in level of the water
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If the radius of the base of a right circular cylinder is halved, keeping the height same, find the ratio of the volume of the reduced cylinder to that of the original cylinder.
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New volume of cylinder
Ratio
Four cubes of volume \(125\ cm^3\) each are joined end to end, in a row. Find the surface area and volume of the resutling cuboid (see fig.)
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A cylindrical pipe has inner diameter of 4 cm and water flows through it at the rate of 20 m per minute. How long would it take to fill a conical tank, with diameter of base as 80 cm and depth 72 cm?
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Time required
A hemispherical bowl of internal diameter 36 cm. is full of liquid. This liquid is to be filled in cylindrical bottles of radius 3 cm and height 6 cm. How many such bottles are required to empty the bowl?
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Volume of liquird in hemispherical bowl
Volume of liquid filled in are cylindrical bottle
Number of bottles
Solid spheres of diameter 6 cm are dropped into a cylindrical beaker containing some water and are fully submerged. If the diameter of the beaker is 18 cm and the water rises by 40 cm, find the number of solid spheres dropped in the water.
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Volume of sphere
Volume of rises in water level
A building is in the form of a cylinder surmounted by hemispherical dome. The base diameter of the dome is equal of \(\dfrac{2}{3} \) of the total height of the building. Find the height of the building, if it contains \( 67\dfrac{1}{21}m^3\) of air.
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A/Q
Height of building
The given figure shows a solid consisting of a cylinder with a cone at one end and a hemisphere at the other end. Common radius = 3.5 cm, the height of the cylinder = 6.5 cm and total height = 12.8 cm. Calculate the volume.
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Height of cone
Volume
How many cubic centimetres of iron is required to construct an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm, provided the thickness of the iron is 1.5 cm. If one cubic centimetre of iron weighs 7.5 gm, find the weight of the box.
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External volume
Internal length
Internal breadth
Internal height
Volume
Volume of iron used
Weight of the box
Water flows through a cylindrical pipe whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour ?
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Volume of cylinder
In 30 minutes volume of water is
Volume of cylinder
A cylindrical vessel is filled with sand and this vessel is emptied on the ground and a conical heap of sand is formed. If the base radius and height of the vessel are 18 cm and 32 cm respectively and the height of the conical heap is 24 cm, find the radius and the stant height of the heap
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Volume of cylinder
Volume of cone
A/Q
The radius of the base of a right circular cone is r. It is cut by a plane parallel to the base at a height h from the base. The distance of the boundary of the upper surface from the centre of the base of the frustum is \(\sqrt{h^2+\dfrac{r^2}{9}} \) Show that the volume of the frustum is \(\dfrac{13}{\sqrt{27\ \pi r^2h}} \)
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Volume of frustum
Water is flowing at the rate of 10 m/min through a cylindrical pipe 5 mm in diameter into a conical vessel whose base diameter is 40 cm and depth 24 cm. In what time will the vessel be filled ?
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Volume of conical vessel
Amount of water
Time
A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone.
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Volume of water left = Volume of cylinder – Volume of cone
The height of a cone is 16 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be \(\dfrac{1}{8} \) of the volume of the given cone, at what height above the base is the section made?
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Volume of big cone
Volume of small cone
…(1)
But
So eqn (1) be cones
height above the base
An open metallic bucket is in the shape of frustum of a cone mounted on a hollow cylindrical base made of metallic sheet. If the diameters of the two ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 30 cm, and that of the cylindrical portion is 6 cm, find the area of the metallic sheet used to make the bucket. Also, find the volume of water it can hold.
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Area of circular base
CSA of cylinder
Area of metallic sheet
The dimensions of a cuboidal box are \(16\ cm \times 8\ cm \times 8\ cm\). 16 glass spheres each of radius 2 cm are packed into this box and then the box is filled with a liquid. Find the volume of the liquid filled in the box.
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Volume of cuboidal box
Volume of sphere
Volume of water in the cuboidal box
A hemispherical tank full of water is emptied by a pipe at the rate of \(3\dfrac{4}{7} \) litres per second. How much time will it take to empty half the tank, if it is 3 m in diameter?
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Volume of tank
Volume of water to be emptied
Time taken to empty litres