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Three cubes are placed adjacent to each other in a row. Find the ratio of the total surface area of the cuboid thus formed to the sum of the surface areas of the three cubes.
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It costs \(\text{Rs}\ 2200\) to paint the inner curved surface of a cylindrical vessel \(10\ m\) deep. If the cost of painting is at the rate of \(\text{Rs}\ 20/m^2\), find the radius of the base.
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CSA
What length of tarpaulin 3 wide will be required to make conical tent of height 8 m and base radius 6m ? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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CSA
Extra length
length
width
Area of sheet = CSA of tent
A right triangle ABC with sides 5 cm, 12cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.
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Volume
A cylinder of maximum volume is cut off from a solid cuboid with square box of side 14 cm and height 20 cm. Find the volume of metal wasted.
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Volume of cylinder
Volume of cuboid
Volume of metal wasted
A conical tent is 5 m high and 24 m in diameter. Find the cost of canvas used in making the tent at the rate of Rs 7 per sq m.
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CSA
Cost
A hemispherical bowl of inner diameter 10 cm has thickness 1 cm. The cost of painting 1 sq. cm is Rs. 2 Find the cost of painting the vessel all over \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Inner surface area
outer surface area
Area of ring
TSA
Cost of painting
The inner diameter of a cylindrical pipe is \(24\ cm \) and its outer diameter is \(28\ cm \). The length of the pipe is \(35\ cm \). Find the mass of the pipe, if \(1\ cm^3 \) of material used to make pipe weights \(0.6\ gm \).
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Volume
Twenty seven solid iron spheres, each of radius 2 cm are melted to form a new solid sphere. What will be the surface area of the new sphere ?
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Volume of smaller sphere
Total number of cubes
Volume of big sphere
Surface area
A school provides milk to the students daily in cylindrical glasses of diameter 7 cm. If the glass is filled with milk upto the height of 12 cm, find how many litres of milk is needed to serve 1600 students. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Volume
Volume of 1600 cylindrical glass
The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the volume of wood used. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Volume of wood
Hameed has built a cubical water tank with lid with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base covered with square tiles of side 25 cm each. How many tiles will be required ?
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Length of the outer edge
Surface area
Area of the tile
Number of tiles
A village having a population of 4000 requires 150 litres of water per head per day. It has a tank measuring \(20m \times 15m \times 6m\). How many days will the water of this tank last ?
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Volume of cuboid
litres
water required by village litres
Number of days
A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute ?
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Speed of river in metre per minute
Breadth , height
Volume
litres
A cylindrical tub of radius 16 cm contains water to a depth of 30 cm. A spherical iron ball is dropped into the tub and thus level of water is raised by 9 cm. What is the radius of the ball ?
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The capacity of a closed cylindrical vessel of height 1m is 15.4 litres. How many square metres of metal sheet would be needed to make it ? \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Capacity of the cylinder
TSA
A hemispherical bowl is made of steel 0.25 cm thick The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Outer radius
outer curved surface area
The diameter of a metallic ball is \(21\ cm\). What is the mass of the ball, if the density of the metal is \(5\ gm\ per\ cm^3\)?
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Radius
volume
The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10 m, how much concrate mixture would be required to build 14 such pillars ?
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volume of concrete in 1 cylindrical piller
volume of concrete in 14 cylindrical piller
The cost of a painting the total outside surface of a closed cylindrical oil tank at 60 paise per sq. dm is Rs 237.60. The height of tank is 6 times the radius of base of tank. Find the volume of the cylindrical tank correct to two decimal places. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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TSA
cost of painting
A/Q
volume of the cylinder
The surface area of a sphere of radius 5 cm is five times the area of curved surface of a cone of radius 4 cm. Find the height and volume of cone. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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volume
A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is \(17.6\ m\), find the cost of painting it, given the cost of painting is \(Rs\ 5\ per\ 100\ cm^2\).
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CSA
cost of painting
At a fair, a stall keeper in one of the food stalls has a large cylindrical vessel of base radius 15 cm filled up to a height of 32 cm with orange juice. The juice is filled in small cylindrical glass of radius 3 cm up to a height of 8 cm and sold at Rs 10 each. How much money does the stall keeper receive by selling the juice completely?
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Volume of juice in the vessel
volume of juice in 1 glass
Number of glasses
Money received by selling 100 glass
Volume of a right circular cone is \(\dfrac{2200}{7}\ cm^3 \) and its diameter is 10 cm. Find its curved surface area. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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volume
CSA
A storage tank is in the form of a cube. When it is full of water the volume of water is \(15.625\ m^3\). If the present depth of water is \(1.3\ m\), find the volume of water used.
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where is side of a cube
Height of water used
volume of water used
A classroom is \(10\ m \) long, \(6.4\ m \) wide and \(5\ m \) high. If each student be given \(1.6\ m^2\) of the floor area how many students can be accomodated in the room ? How many cubic metres of air each student will get ?
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Number of students
volume of room
Area required by each students
We want to make a closed cylindrical storage tank of height 2 m and base diameter 210 cm from a metal sheet. How many square metres of the sheet are required for the purpose ?
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Radius
Area of sheet required
The height and base diameter of a conical tent is 16 m and 24 m respectively. Find the cost of canvas required to make it at the rate of \(Rs\ 210\ per\ m^2\)?
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CSA
cost
A rectangular sheet of paper \(66\ cm \times 20\ cm\) is rolled along its length to form a cylinder. Find the radius and volume of the cylinder.
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volume
The volume of a right circular cylinder is 3850 cubic cm. Find its height, if itโs diameter is 14 cm
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The paint in a certain container is sufficient to paint an area equal to \(9.375\ m^2\). How many bricks of dimensions \(22.5\ cm \times 10\ cm \times 7.5\ cm\) can be painted out of this container ?
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Area that can be painted by the container
Total surface area of one brick
Number of bricks
The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find :
(i) Its inner curved surface area
(ii) The cost of plastering this curved surface at the rate of \(Rs\ 40\ per\ m^2\).
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Inner CSA
cost of plastering
The sum of the radius of the base and height of a solid cylinder is \(37\ m \). If the total surface area of the cylinder is \(1628\ m^2\), find the volume of the cylinder \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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volume
Find the volume of metal used in making a hollow hemispherical bowl with internal and external diameters 4 cm and 10 cm respectively. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Volume of metal used = outer volume – Inner volume
A hemispherical bowl with radius 6 cm is filled with water. If the water is transferred into cylindrical vessel of base radius 3 cm, find the height to which the water rises in the cylindrical vessel. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Volume of hemisphere = volume of cylinder
In a river 2 m deep and 30 m wide, water is flowing at the rate of 1 km per hour. How much water will flow in 10 minutes ?
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In 60 minutes water flow
In 1 minute water
In 10 minutes water flow
Volume
A solid right circular cylinder of radius 8 cm and height 3 cm is melted to make a cone of height 3 times that of cylinder. Find the curved surface area of the cone \((use\ \sqrt{145}=12) \)
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Height of cone = 3 times height of cylinder
A/Q volume of cylinder = volume of cone
A hemispherical bowl of internal diameter 36 cm contains a liquid. This liquid is filled in cylindrical bottles of radius 3 cm and height 6 cm. How many bottles are required to empty the bowl ?
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Volume of cylindrical bottles
volume of bowl
Number of bottles
(approx)
How many solid spheres of diameter 6 cm can be cast out of a solid cylinder with radius of the base 9 cm and height 40 cm ? \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Volume of cylinder
Number of sphere
A hollow cylindrical pipe 21 dm long is made of copper. Its outer and inner diameters are 10 cm and 6 cm respectively. Find the volume of the copper used in making the pipe.
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Volume of copper