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The diameter of a cylindrical roller 120 cm long is 84 cm. It takes 500 complete revolutions to level a playground. Find the cost of levelling it at Rs. 7.50 per sq. m.
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cost
From a right circular cylinder with height 8 cm and radius 6 cm, a right circular cone of the same height and base is removed. Find the total surface area of the remaining solid.
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TSA = CSA of cylinder + Area of the base of cylinder + CSA of cone
An iron pipe 20 cm long has exterior diamter 25 cm. If the thickness of the pipe is 1 cm, find the whole surface area of the pipe.
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TSA
A storage tank consists of a circular cylinder, with a hemisphere adjoined on either end. If the external diameter of the cylinder be 1.4 m and its length be 5 m what will be the cost of painting it on the outside at the rate of Rs 10 per square metre ? \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Radius
Height
Surface area of tank
cost
If \(h, c, v\) are respectively the height, the curved surface and the volume of a cone, show that \(3\pi vh^3 – c^2h^2 + 9v^2 = 0\).
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Water in a rectangular reservoir having base \(80\ m \times 60\ m\) is \(6.5\ m\) deep. In what time can the water be emptied by a pipe of which the cross section is a square of side \(20\ cm\), if the water runs through the pipe at the rate of \(15\ km/h\) ?
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flow of water
volume of water
volume of the tank
Time taken
Rain water which falls on a flat rectangular surface of length 6 m and breadth 4 m is transferred into a cylindrical vessel of internal radius 20 cm. What will be the height of water in the cylindrical vessel, if the rainfall is 1 cm?
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Volume of rain fall
A sphere and a right circular cylinder of the same radius have equal volumes. By what percentages does the diameter of the cylinder exceed its height ?
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Volume of cylinder
volume of sphere
A/Q
Percentage difference
The water for a factory is stored in a hemispherical tank whose internal diameter is 14 m. The tank contains 50 kilolitres of water. Water is pumped into the tank to fill to its capacity. Find the volume of the water pumped into the tank.
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capacity of the tank
volume of water pumped
A vessel is in the form of an inverted cone. Its height is 8 cm and radius of its top which is open is 5 cm. It is filled with water up to the brim. When lead shots of radius 0.5 cm are dropped into the vessel, of the water flows out. Find the number of lead shots dropped in.
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Volume of the cone
volume of water which flows out
volume of spherical ball
Number of lead shots
A conical vessel with radius 5 cm and height 24 cm is full of water. Water is emptied into a cylindrical vessel of radius 10 cm. Find the height to which the water raises. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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A hemispherical dome of a building and the walls of the cylindrical shaped building needs to be painted on inside. If the circumference of the base of the dome is 17.6 m, find the cost of painting it, if the total height of the building is 9.8 m and cost of painting it is \(Rs\ 2\ per\ 100\ cm^2\).
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Height of cylindrical wall
CSA of dome + CSA of cylinder
cost of painting
A powder tin has square base with side 8 cm and height 13 cm and another is cylindrical with base radius 7 cm and height 15 cm. Which of the two has more capacity ? How much is the difference in their capacities ? \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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A cylinder has more capacity
Difference
A right angled triangle with sides 5 cm, 12 cm, 13 cm is revolved around 5 cm side and then around 12 cm side. Find the volume of solid in both the cases. Also, find the ratio of their volumes.
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On revolving along
volume
on revolving along side
volume
Ratio
A man built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of tank excluding the base covered with square tiles of side 25 cm. Find how much he would spend for the tiles, if cost of tiles is Rs 480 per dozen.
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Surface area of tank
Area of one square tile
Number of tiles
cost of 180 tiles
Monica has a piece of canvas whose area is \(551\ m^2\). She uses it to have a conical tent made, with base radius of \(7\ m\). Assuming that all the stitching margins and the wastage incurred while cutting, amounts to approximately \(1\ m^2\), find the volume of the tent that can be made with it.
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Area of canvas
volume
A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of Rs 498.96. If the cost of whitewashing is Rs 2.00 per square metre, find the following :
(i) inside surface area of the dome.
(ii) volume of the air inside the dome.
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Inner surface area
volume of air
Harry has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of sides 25 cm. Find how much he would spend for the tiles, if the cost of the tiles is Rs. 36 per dozen.
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Area of one wall
Area of 5 walls
Number of tiles
cost
A cube and cuboid have same volume. The dimensions of the cuboid are in the ratio 1 : 2 : 4. If the difference between the cost of polishing the cube and cuboid at the rate of \(Rs.\ 5\ per\ m^2\) is \(Rs\ 80\), find their volumes.
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volume of cuboid
Difference
Side of cube , volume
cuboid
Circumference of the base of a cylinder, open at the top, is 132 cm. The sum of radius and height is 41 cm. Find the cost of polishing the outer surface area of cylinder at the rate Rs 10 per square dm (decimetre). \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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cost
A juice seller in a marriage party has a cylindrical vessel with base radius 25 cm and height 40 cm full of juice. He gives the same in small glasses of radius 5 cm and height 10 cm. How many oranges are required for the bigger vessel to fill it completely if to fill one small glass two oranges are required ?
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Radius of big cylindrical vessel
Height of big cylindrical vessel
volume
volume of each cylindrical vessel
Number of small glass
Number of oranges required
A tent is in the shape of a right circular cylinder upto a height of 3 m and a cone above it. The maximum height of the tent above ground is 13.5 m. Calculate the cost of painting the inner side of the tent at the rate of Rs 3 per sq. m., if the radius of the base is 14 m.
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CSA of cylinder
Height
CSA of cone
Total area
cost of painting
A wall of length \(10\ m\) was to be built across an open ground. The height of the wall is \(4\ m \) and thickness of the wall is \(24\ cm \). If this wall is to be built up with bricks whose dimensions are \(24\ cm \times 12\ cm \times 8\ cm\), how many bricks would be required ?
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Volume of the wall
volume of each brick
Number of bricks (approx)
A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical ball is dropped into the tub raising the level of water by 6.75 cm.What is the radius of the ball ? \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Volume of cylinder
…(1)
volume of sphere …(2)
A/Q
Metal spheres, each of radius \(2\ cm \) are packed into a rectangular box of dimensions \(16\ cm \times 8\ cm \times 8\ cm\). When \(16 \) spheres are packed in the box, it is filled with preservative liquid. Find the volume of this liquid to the nearest integer.
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Volume of cubical box
volume of sphere
volume of 16 sphere
volume of liquid
The difference between the outer lateral surface area and inner lateral surface area of a cylindrical metallic pipe \(28\ cm \) long is \(176\ cm^2\). Find the outer and inner radii of the pipe, if the pipe is made of \(352\ cm^3\) of metal.
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A/Q
outer LSA – Inner LSA = 176
External volume – Internal volume = 352
….(2)
on solving
A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.
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Volume of graphite
volume of wood = volume of pencil – volume of graphite
Volume of pencil
volume of wood
A corn cob, shaped like cone has the radius of the base as 2.1 cm and height as 20 cm. If each 1 sq. cm of the surface of cob carries an average of 4 grains, find how many grains you would find in the entire cob?
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CSA
Total number of grains on the corn cob
A cone of radius \(7\ cm \) has a curved surface area \(550\ cm^2 \). Find its volume. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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volume