An iron pillar consists of a cylindrical portion portion of 2.8m height and 20 cm in diameter and a cone of 42 cm height surmounting it. Find the weight of the pillar if 1 cm3 of iron weight 7.5 g.
Answers
Given data : An iron pillar consists of a cylindrical portion of 2.8 m height and 20 cm in diameter and a cone of 42 cm height surmounting it.
To find : Find the weight of the pillar if 1 cm³ of iron weight 7.5 gram.
Solution : Here, a/c to question;
➜ Height of the cylindrical portion = 2.8 m = 280 cm
➜ Diameter of the cylindrical portion = 20 cm
➜ Radius of the cylindrical portion = diameter/2 = 20/2
= 10 cm
➜ Height of the conical portion = 42 cm
We use formula of volume of the cylinder to find out volume cylindrical portion;
➜ volume of cylindrical portion = πr²h
➜ volume of cylindrical portion = 22/7 * 10² * 280
➜ volume of cylindrical portion = 22/7 * 100 * 280
➜ volume of cylindrical portion = 2200/7 * 280
➜ volume of cylindrical portion = 2200 * 40
➜ volume of cylindrical portion = 88000 cm³
By formula of volume of cone;
➜ volume of conical portion = 1/3 π r² h
Here radius of cylindrical portion and conical portion is equal because conical portion is mounted on cylindrical portion.
➜ volume of conical portion = 1/3 π r² h
➜ volume of conical portion = 1/3 * 22/7 * 10² * 42
➜ volume of conical portion = 22/21 * 100 * 42
➜ volume of conical portion = 22/21 * 100 * 42
➜ volume of conical portion = 2200/21 * 42
➜ volume of conical portion = 2200 * 2
➜ volume of conical portion = 4400 cm³
Now,
➜ Volume of the pillar = volume of cylindrical portion + volume of conical portion
➜ Volume of the pillar = 88000 + 4400
➜ Volume of the pillar = 92400 cm³
Now,
➜ Weight of pillar = Volume of the pillar * weight of 1 cm³ iron
➜ Weight of pillar = 92400 * 7.5
➜ Weight of pillar = 693000 gram
Answer : Hence, the weight of the pillar is 693000 gram.
{More info : 1 kg = 1000 gram
so, 693000 gram = 693000/1000 kg = 693 kg}
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