A Square With Area of 16 Cm^2 Is Rotated to Form Cylinder. What Is the Volume of the Cylinder?

In this chapter, we provide RD Sharma Course 8 Solutions Affiliate 22 Mensuration (Surface Expanse and Volume of a Right Round Cylinder)  Ex 22.ii for English medium students, Which volition very helpful for every student in their exams. Students tin can download the latest RD Sharma Grade 8 Solutions Chapter 22 Mensuration (Surface Area and Volume of a Right Circular Cylinder)  Ex 22.2 pdf, costless RD Sharma Class 8 Solutions Chapter 22 Mensuration (Surface Area and Book of a Correct Circular Cylinder)  Ex 22.2 book pdf download. Now you will become step by footstep solution to each question.

Textbook	NCERT
Grade	Grade viii
Subject	Maths
Chapter	Chapter 22
Chapter Name	Mensuration (Surface Expanse and Book of a Right Circular Cylinder)
Exercise	Ex 22.2

RD Sharma Solutions for Class 8 Chapter 22 Mensuration (Surface Surface area and Book of a Right Circular Cylinder) Ex 22.two Download PD

Question one.
Find the volume of a cuboid whose
(i) r = 3.five cm, h = forty cm
(two) r = 2.eight m, h = fifteen thousand
Solution:
(i) Radius (r) = iii.5 cm
Height (h) = 40 cm
Volume of cylinder = πr^twoh

Question 2.
Find the volume of a cylinder, if the diameter (d) of its base and its altitude (h) are:
(i) d= 21 cm, h = ten cm
(ii) d = 7 m, h = 24 thou.
Solution:
(i) Diameter (d) = 21 cm

Question three.
The area of the base of a right circular cylinder is 616 cm3 and its height is 25 cm. Find the volume of the cylinder.
Solution:
Base surface area of cylinder = 616 cm²
Tiptop (h) = 25 cm.
∴ Volume = Area of base x summit
= 616 ten 25 cm³ = 15400 cm^three

Question 4.
The circumference of the base of a cylinder is 88 cm and its height is fifteen cm. Detect the book of the cylinder.
Solution:
Circumference of the base of operations of cylinder = 88 cm
Let r exist the radius

Question 5.
A hollow cylindrical pipe is 21 dm long. Its outer and inner diameters are 10 cm and 6 cm respectively. Notice the volume of the copper used in making the pipage.
Solution:
Length (Top) of hollow cylindrical pipe = 21 dm = 210 cm
Inner diameter = 6 cm
Outer diameter = 10 cm

Question six.
Notice the (i) curved surface area (two) total surface area and (3) book of a right circular cylinder whose height is 15 cm and the radius of the base is seven cm
Solution:
Radius of the cylider (r) = vii cm
and superlative (h) = 15 cm
(i) Curved surface area = 2πrh

Question 7.
The diameter of the base of operations of a right circular cylinder is 42 cm and its peak is 10 cm. Discover the volume of the cylinder.
Solution:
Bore of the base of cylinder = 42 cm

Question viii.
Find the book of a cylinder, the bore of whose base is 7 cm and top existence 60 cm. Also, find the capacity of the cylinder in litres.
Solution:
Diameter of cylinder = 7 cm

Question 9.
A rectangular strip 25 cm x 7 cm is rotated about the longer side. Discover the book of the solid, thus generated.
Solution:
Size of rectangular strip = 25 cm x 7 cm
By rotating, almost the longer side, we notice a correct round cylinder,
then the radius of cylinder (r) = 7 cm

Question x.
A rectangular sheet of paper 44 cm x twenty cm, is rolled along its length to form a cylinder. Find the book of the cylinder then formed.
Solution:
Size of canvas of newspaper = 44 cm 10 20 cm
Past rolling forth length, a cylinder is formed in which circumference of its base = xx cm
and elevation (h) = 44 cm

Question eleven.
The volume and the curved surface area of a cylinder are 1650 cm3 and 660 cm2 respectively. Find the radius and elevation of the cylinder.
Solution:
Volume of cylinder = 1650 cm^three
and curved surface area = 660 cm²
Let r exist the radius and h be the acme of the cylinder, and then

Question 12.
The radii of two cylinders are in the ratio ii :3 and their heights are in the ratio 5 : 3. Calculate the ratio of their volumes.
Solution:
Ratio in radii = 2:3
and in heights = v:3
Let r₁,h_one and r₂, h₂ are the radii and heights of two cylinders respectively.

Question 13.
The ratio between the curved expanse and the total surface area of a right circular cylinder is 1 : 2. Observe the volume of the cylinder, if its total expanse is 616 cm².
Solution:
Ratio in curved surface are and total surface expanse =i : 2
Allow r be the radius and h be the height.
Then 2πrh : 2πr (h + r)= 1 : 2

Question 14.
The curved surface area of a cylinder is 1320 cm2 and its base has bore 21 cm. Find the book of the cylinder.
Solution:
Curved surface expanse of a cylinder = 1320 cmⁱⁱ
Diameter of base of operations = 21 cm

Question 15.
The ratio between the radius of the base of operations and the height of a cylinder is 2 : 3. Find the total surface area of the cylinder, if its volume is 1617 cm³.
Solution:
Ratio between radius and height of a cylinder = 2:three
Book = 1617 cmⁱⁱⁱ
Let r exist the radius and A be the summit of the cylinder, then

Question sixteen.
The curved surface area of a cylindrical pillar is 264 m² and its book is 924 m³. Notice the bore and the height of the pillar.
Solution:
Let r be the radius and A be the height of the cylinder, and so
2πrh = 264 …(i)
and πr2h= 924 …(ii)
Dividing (ii) by (i),

Question 17.
Two circular cylinders of equal volumes take their heights in the ratio 1 : 2. Find the ratio of their radii.
Solution:
Volumes of two cylinders are equal.
Let r1, r2 are the radii and h_i, h₂ are their heights, then

Now, volume of first cylinder = πr₁ ^twoh_i
and Volume of second cylinder = πr₂ ²h₂
Their volumes are equal

Question 18.
The height of a right circular cylinder is x.five one thousand. Three times the sum of the areas of its 2 circular faces is twice the area of the curved surface. Find the book of the cylinder.
Solution:
Height of cylinder (A) = 10.5 yard.
Allow r be the radius, and then
Sum of areas of two circular faces = 2π²
and curved surface area = 2πrh
According to the status,

Question 19.
How many cubic metres of earth must be dug-out to sink a well 21 m deep and half dozen m diameter ?
Solution:
Diameter of well = 6 grand

Question 20.
The trunk of a tree is cylindrical and its circumference is 176 cm. If the length of the trunk is 3 m, find the volume of the timber that can exist obtained from the body.
Solution:
Circumference of cylindrical trunk = 176 cm

Question 21.
A well is dug twenty m deep and it has a diameter of vii m. The world which is so dug out is spread out on a rectangular plot 22 m long and 14 m wide, what is the peak of the platform so formed ?
Solution:
Bore of the well = vii g
∴ Radius (r) = 72 m
Depth (h) = 20 k
= Volume of earth dug out = πr²h

Question 22.
A well with fourteen m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around information technology to a width of 21 m to form an embankment. Find the superlative of the beach.
Solution:
Diameter of the well = xiv m

Question 23.
A cylindrical container with diameter of base 56 cm contains sufficient water to submerge a rectangular solid of fe with dimensions 32 cm 10 22 cm x 14 cm. Notice the rise in the level of the water when the solid is completely submerged.
Solution:
Bore of the base of a cylindrical container = 56 cm

Dimensions of the rectangular solid = 32 cm x 22 cm 10 14 cm
∴ Volume of solid = 32 ten 22 x 14 cmⁱⁱⁱ = 9856 cmⁱⁱⁱ
∴Book of water rose up = 9856 cm³
Let h exist the height of water, then πr²h = 9856

Question 24.
A rectangular sheet of paper 30 cm ten 18 cm can be transformed into the curved surface of a right circular cylinder in two ways Le., either past rolling the paper forth its length or by rolling it along its breadth. Find the ratio of the volumes of the 2 cylinders thus formed.
Solution:
Size of newspaper = 30 cm and eighteen cm.

(i) Past rolling length wise,
The circumference of base = 30 cm

Question 25.
The rain which falls on a roof eighteen yard long and 16.5 g wide is allowed to be stored in a cylindrical tank 8 one thousand in diameter. If it rains 10 cm on a 24-hour interval, what is the ascent of water level in the tank due to it.
Solution:
Length of roof (l) = 18 k
Breadth (b) = sixteen.5 grand
Height of water on the roof = ten cm
∴ Volume of water collected

Question 26.
A Piece of ductile metal is in the form of a cylinder of diameter ane cm and length 5 cm. It is drawnout into a wire of diameter 1 mm. What will be the length of the wire and so formed ?
Solution:
Diameter of ductile metal = 1 cm
and length (h) = 5 cm
and radius (r) = 12 cm

Question 27.
Find the length of 13.2 kg of copper wire of diameter 4 mm when 1 cubic cm of copper weighs 8.iv gm.
Solution:
Weight of wire = 13.two kg
Bore of wire = 4 mm

Question 28.
2.2 cubic dm of brass is to be drawn into a cylindrical wire 0.25 cm in diameter. Find the length of the wire.
Solution:
Book of brass = 2.2 cu.dm
= 2.2 x 10 ten 10 x 10 = 2200 cm²
Diameter of wire = 0.25 cm

Question 29.
The difference between inside and outside surfaces of a cylindrical tube fourteen cm long is 88 sq. cm. If the book of the tube is 176 cubic cm, discover the inner and outer radii of the tube.
Solution:
Let r and R exist the radii of inner and outer surfaces of a cylindrical tube,

Question thirty.
Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of six metres per 2d into a cylindrical tank, the radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes.
Solution:
Diameter of pipe = 2 cm
∴ Radius (r) = 22 = 1 cm = 0.01 one thousand
Length of flow of h2o in 1 2d = 6 m Length of menstruum in xxx minutes = 6 10 30 x 60 1000 = 10800 k
∴ Book of water = πr²h

Question 31.
A cylindrical tube, open at both ends, is to made of metal. The internal diameter of the tube is 10.iv cm and its length is 25 cm. The thickness of the metallic tube is 8 mm everywhere. Calculate the book of the metal.
Solution:
Length of metal tube (h) = 25 cm
Internal diameter = 10.4 cm
∴ Internal radius (r) = 10.42 = 5.2 cm
Thickness of metal = 8 mm = 0.viii cm
∴ Outer radius = 5.2 + 0.8 = 6 cm
Now book of the metal

Question 32.
From a tap of inner radius 0.75 cm, h2o flows at the rate of 7 m per 2d. Detect the volume in litres of water delivered by the pipe in one hour.
Solution:
Inner radius of pipage (r) = 0.75 cm
Rate of water period = 7 chiliad per second
∴ Length of water flow in i hour (h)
= 7 x 3600 chiliad = 25200 m
∴ Volume of water in ane 60 minutes

Question 33.
A cylindrical water tank of diameter 1. four grand and elevation two.1 thousand is being fed by a pipage of diameter 3.v cm through which water flows at the rate of 2 metre per second. In how much time the tank will be filled ?
Solution:
Diameter of cylindrical tank = 1.4 m
∴ Radius (r) = ane.42 = 0.7 thousand
Height (h) = 2.1m.

Question 34.
A rectangular sail of newspaper 30 cm x 18 cm can be transformed into the curved surface of a correct round cylinder in two ways Le. either by rolling the newspaper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinder thus formed.
Solution:
In first case,
By rolling the paper along its length,
the circumference of the base = 30 cm
and top (h) = 18 cm

Note: Run into Q.No. 24 this practise

Question 35.
How many litres of water flow out of a pipage having an area of cantankerous-section of 5 cm2 in ane infinitesimal, if the speed of water in the pipe is 30 cm/sec ?
Solution:
Speed of water = 30 cm/sec
∴ H2o menstruum in i minute = 30 cm 10 sixty = 1800 cm
Area of cross-section = 5 cm^two
∴ Volume of h2o = 1800 x 5 = 9000 cmⁱⁱⁱ
Capacity of h2o in litres = 9000 x l ml

Question 36.
A solid cylinder has a total surface area of 231 cm². Its curved surface area is 23 of the total surface area. Find the volume of the cylinder.
Solution:
Total surface area of a solid cylinder = 231 cmⁱⁱ
Curved surface expanse = 23 of 231 cm² = 2 x 77 = 154 cm²
and surface area of two round faces = 231-154 = 77 cm²
Let r be the radius, so

Question 37.
Find the cost of sinking a tubewell 280 1000 deep, having diameter three grand at the rate of Rs three.sixty per cubic metre. Find also the cost of cementing its inner curved surface at Rs 2.50 per square metre.
Solution:
Diameter of well = 3 m
∴ Radius (r) = 32 g
and depth (h) = 280 g
(i) Volume of earth dug out = πr^twoh

Charge per unit of sinking the well = Rs 3.threescore per m³
∴ Total toll of sinking = Rs 1980 x 3.60 = Rs seven,128
(2) Inner curved surface area = 2πrh

Charge per unit of cementing = Rs ii.50 per mⁱⁱ
∴ Total cost of cementing = Rs 2.50 x 2640
= Rs 6,600

Question 38.
Find the length of 13.2 kg of copper wire of diameter 4 mm, when 1 cubic cm of copper weighs viii.four gm.
Solution:
Note : Run across Q.No. 27 of this exercise

Question 39.
2.ii cubic dm of brass is to be drawn into a cylindrical wire 0.25 cm in bore. Find the length of the wire.
Solution:
Note: Run into Q.No. 28 of this exercise.

Question 40.
A well with x m inside diameter is dug viii.4 thou deep. Earth taken out of information technology is spread all around it to a width of 7.5 m to form an beach. Notice the height of the embankment.
Solution:
Diameter of the well = x m

Question 41.
A hollow garden roller, 63 cm wide with a girth of 440 cm, is fabricated of 4 cm thick iron. Find the volume of the iron.
Solution:
Width of roller (h) = 63 cm.

Outer circumference of roller = 440 cm

Question 42.
What length of a solid cylinder ii cm in diameter must be taken to recast into a hollow cylinder of length sixteen cm, external diameter twenty cm and thickness 2.5 mm ?
Solution:
Length of hollow cylinder (h) = 16 cm
External diameter = 20 cm
∴ External radius (R) = 202 = x cm
Thickness of iron = 2.5 mm
∴ Internal radius (r) = 10 – 0.25 = 9.75 cm
∴ Volume of fe = πh (Rⁱⁱ – r^two)

Question 43.
In the eye of rectangular field measuring 30 m x xx grand, a well of 7 m diameter and x m depth is dug. The earth so removed is evenly spread over the remaining part of the field. Find the height through which the level of the field is raised.
Solution:
Diameter of well = 7 m
∴ Radius (r) = 72 m
Depth (h) = 10 m.
∴ Volume of earth dug out = πr²h

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