A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm3 of iron has approximately 8 g mass. (Use π = 3.14)
Solution:
The figure drawn below is to visualize the iron pole.
We can see that,
Volume of the solid iron pole = volume of larger cylinder + volume of smaller cylinder
Mass of iron in the pole = 8 g × volume of the solid iron pole in cm3
We will find the volume of the solid by using formula;
Volume of the cylinder = πr2h where r and h are the radius and height of the cylinder respectively
Radius of larger cylinder, R = 24 cm/2 = 12 cm
Height of larger cylinder, H = 220 cm
Radius of smaller cylinder, r = 8 cm
Height of smaller cylinder, h = 60 cm
Volume of the solid iron pole = volume of larger cylinder + volume of smaller cylinder
= πR2H + πr2h
= π(12 cm × 12 cm × 220 cm + 8 cm × 8 cm × 60 cm)
= 3.14 × (31680 cm3 + 3840 cm3)
= 3.14 × 35520 cm3
= 111532.8 cm3
Mass of 1 cm3 iron is 8 g
Mass of iron in the pole = 8 g × volume of the solid iron pole
= 8 g × 111532.8
= 892262.4 g
= 892262.4/1000 kg
= 892.2624 kg
Thus, the mass of iron in the pole is 892.26 kg.
☛ Check: NCERT Solutions Class 10 Maths Chapter 13
Video Solution:
A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm3 of iron has approximately 8 g mass. (Use π = 3.14)
NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2 Question 6
Summary:
A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. The mass of the pole, given that 1 cm3 of iron has approximately 8 g mass is 892.26 kg.
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