Surface Areas and Volumes: 9 Math
NCERT Exercise 13.6: 9th math
Important Formula
Volume of a Cylinder = Area of circular base × height
⇒ Volume of a Cylinder
=ℼ r2 h
Where, r = radius of base of the cylinder and h = height of the cylinder
NCERT Exercise 13.6 Questions and Answers
Assume `pi=22/7`, unless stated otherwise.
Surface Areas And Volumes Class nine Math NCERT Exercise 13.6 Question (1) The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000cm3 1/)
Solution
Given, circumference of the base of the cylinder = 132 cm
And, height of the cylinder = 25 cm
Therefore, litres of water can be hold by cylinder = ?
Calculation of radius of base of the cylinder
We know that, circumference of a circle
= 2 &8508; r
Thus, circumference of the given cylinder
⇒ 132 cm = 2 × `22/7` × r
`=>r = (132 cm xx7)/44`
⇒ r = 3 cm xx 7
⇒ r = 21 cm
Thus, radius (r) of the given cylinder = 21 cm
Now, we know that, Volume of a cylinder
= ℼ r2 h
Thus, volume of the given cylinder `=22/7xx(21cm)^2\xx25cm`
`=22/7xx21cmxx21cmxx25cm`
= 22 × 3 cm × 21cm × 25 cm
= 66 cm × 25 cm
= 34650 cm3
Thus, volume of cylinder = 34650 cm3 = volume of water can be hold by the cylinder
Thus, volume of water can be hold by the cylinder
= 34650 cm3
Now, we know that, 1000 cm3 = 1 litre
Therefore, 1 cm3 `=1/1000\ l`
Therefore, 34650 cm3 `=1/1000xx34650\ l`
= 34.65 litre
Thus, volume of water can be hold by the given cylinder = 34.65 litre Answer
Surface Areas And Volumes Class nine Math NCERT Exercise 13.6 Question (2) 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 mass of the pipe. If 1 cm3 of wood has a mass of 0.6 g.
Solution
Given, Inner diameter of the cylindrical wooden pipe = 24 m
Therefore, Inner radius (r) = 24/2 = 12 cm
And, Outer diameter of the pipe = 28 cm
Therefore, Outer radius (R) = 28/2 = 14 cm
And, length of the pipe = 35 cm
And, mass of 1 cm3 of given wooden pipe = 0.6 g
Therefore, mass of given pipe = ?
Now, volume of wood used in the pipe = outer volume of the pipe – inner volume of the pipe
= ℼ R2 h – ℼ r2 h
= ℼ h (R2 – r2)
= `22/7` × 35cm ((14cm)2 – (12cm)2)
= 22 × 5 cm(196 cm2 – 144 cm2)
= 110 cm × 52 cm2
= 5720 cm3
Thus, volume of wood used in the given pipe
= 5720 cm3
Now, since mass of 1 cm3 of wood = 0.6 gm
Therefore, mass of 5720 cm3 = 0.6 gm × 5720
= 3432 gm or 3.432 kg
Therefore, mass of the given pipe = 3432 gm or 3.432 kg Answer
Surface Areas And Volumes Class nine Math NCERT Exercise 13.6 Question (3) A soft drink is available in two packs – (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and (ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?
Solution
Given,
For Rectangular Tin Can (cuboid)
Length of the tin can = 5 cm,
Width of the tin can = 4 cm
And, Height of the tin can = 15 cm
For Cylindrical Plastic Pack
Diameter of base = 7 cm
Therefore, radius (r) of the base = 7/2 cm
And, height of the cylinder = 10 cm
Thus, which container has greater capacity and by how much?
Calculation for rectangular tin can (cuboid)
We know that, Volume of a cuboid `= lbh`
Therefore, volulme of the given cuboidal tin can
= 5 cm × 4 cm × 15 cm
= 20 cm2 × 15 cm
= 300 cm3
Thus, volume of the given rectangular tin can = 300 cm3
Calculation for cylindrical plastic container
We know that Volume of a cylinder
= ℼ r2 h
Thus, volume of the given cylinder `=22/7xx(7/2cm)^2 xx 10 cm`
`= 22/7xx7/2cmxx7/2cmxx10cm`
= 11 × × 1 cm × 7 cm× 5 cm
= 77 cm2 × 5 cm
= 385 cm3
Thus, volume of the given cylindrical plastic container
= 385 cm3
Now, it is clear that volume of plastic container is greater
And, difference between volume of plastic container and the volume of the rectangular tin can
= 385 cm3 – 300 cm3 = 85 cm3
Now, since volume of cylinder is greater than volume of cuboid by
= 85 cm3
Thus, volume of plastic cylindrical container is greater than that of rectangular container by 85 cm3 Answer
Surface Areas And Volumes Class nine Math NCERT Exercise 13.6 Question (4) If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, then find (i) radius of its base (ii) its volume (use ℼ = 3.14)
Solution
Given, lateral surface area of the cylinder = 94.2 cm2
And, Height of the cylinder = 5 cm
And, ℿ = 3.14
Therefore, radius and volume of the given cylinder = ?
(i) radius of the base of the given cylinder
We know that, lateral surface area of a cylinder
= 2 ℼ r h
Therefore, lateral surface area of the given cylinder
= 2 × 3.14 × r × 5cm
⇒ 94.2 cm2 = 6.28 × r × 5 cm
⇒ 94.2 cm2 = 31.4 cm r
`=>r = (94.2 cm^2)/(31.4 cm)`
⇒ r = 3 cm
Thus, radius of the given cylinder
= 3 cm Answer
(ii) Volume of cylinder
We know that, Volume of a cylinder
= ℼ r2 h
Thus, volume of the given cylinder
= 3.14 × (3 cm)2 × 5 cm
= 3.14 × 9 cm2 × 5 cm
= 3.14 × 45 cm3
= 141.3 cm3
Thus, volume of the given cylinder
= 141.3 cm3
Thus, radius of the given cylinder = 3 cm and volume of the given cylinder = 141.3 cm3 Answer
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