S.chand books class 8 maths solution chapter 27 Volume and Surface Area of Solids exercise 27 C

 EXERCISE 27 C

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Q1 | Ex-27C | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

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Question 1

Find the volume of each of the following cylinders whose:
(i) Radius of base = 10cm
Height = 14 cm

(ii) Radius of base = 21cm
Height = 30 cm

(iii) Radius of base = 10.5cm
Height = 35 cm

Sol :

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Q2 | Ex-27C | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

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Question 2

The area of the base of a circular cylinder is 35 cm² and its height 12 cm. What will be its volume?

Sol :

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Q3 | Ex-27C | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

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Question 3

If the capacity of a cylindrical tank is 1848 m3 and the diameter of the base is 14 m, then what is the depth of the tank?

Sol :

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Q4 | Ex-27C | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

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Question 4

If the volume of a right circular cylinder with its height equal to the radius is $25\dfrac{1}{7}~cm^3$ , then find the radius of the base of the cylinder.

Sol :

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Q5 | Ex-27C | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

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Question 5

Total surface area of a right circular cylinder is 1540cm² . If its height is four times the radius, then find the volume of the cylinder.

Sol :

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Q6 | Ex-27C | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

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Question 6

A drainage tile is a cylindrical shell 21cm long. The inside and outside diameters are 8cm and 10cm respectively . What is the volume of clay required for the tile ?

Sol :

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Q7 | Ex-27C | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

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Question 7

The volume of the metal of a cylindrical pipe is 748 cm³. The length of the pipe is 14 cm and the extemal radius is 9cm. What is the thickness of metal in the pipe ?

Sol :

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Q8 | Ex-27C | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

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Question 8

Two right circular cylinders of equal volume have their heights in the ratio 1 : 2. What is the ratio of their radii?

Sol :

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Q9 | Ex-27C | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

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Question 9

Water is being pumped out through a circular pipe whose internal diameter is 7 cm. If the f‌low of water is 12 cm/s. How many litres of water is being pumped out in an hour?

Sol :

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Q10 | Ex-27C | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

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Question 10

If a solid right circular cylinder made of iron is heated to increase its radius and height by 1% each , then by how much per cent does the volume of the solid increase ?

Sol :

We know that, if 'r' and 'h' be the radius and height of a right circular cylinder, then its volume will be

V=πr²h

Now, if radius and height are increased by 1%, then the new radius and height will be

r' h=r+1%×r

=r+0.01r=1.01r

h' =h+1%×h

=1.01h

Therefore, new volume will be

V' =πr'²h'=π(1.01r)r²(1.01h)

=1.030301πr²h

So, increase in the volume is

I=V' -V=1.030301V-V

=0.030301V

Thus, percentage of increase in volume will be
I% = 0.030301 × 100%=3.0301%.

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Q11 | Ex-27C | Class 8| S.Chand | Composite maths |Volume and Surface Area of Solids| myhelper

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Question 11

A well 20m in diameter is dug 18m deep and earth taken out is spread all around it to a width of 5m to form a embankment. What is the height of the embankment ?

Sol :