Question

the thickness of a metallic tube is 1cm and the inner diameter of the tube is 12cm. find the weight of 1m long tube, if the density of the metal is 7.8g/cm³​

Answer 1

Given data : The thickness of a metallic tube is 1 cm and the inner diameter of the tube is 12 cm. the density of the metal is 7.8 g/cm³.

To find : find the weight of 1m long tube.

Solution : Let, shapes of metalic tube be cylindrical.

• Diameter of the tube, d = 12 cm
• Inner radius of the tube, = d/2 = 12/2 = 6 cm
• Thickness of the tube = 1 cm
• Height of the tube = 1 m = 100 cm
• density of the metallic tube = 7.8 g/cm³

Now,

➜ outer radius of the tube = Inner radius + thickness

➜ outer radius of the tube = 6 + 1

➜ outer radius of the tube = 7 cm

Now, here

➜ r² = {(outer radius)² - (Inner radius)²}

➜ r² = {(7)² - (6)²}

➜ r² = 49 - 36

➜ r² = 13 cm

Now, by formula of volume of cylinder

➜ volume of the tube = π * r² * h

➜ volume of the tube = 22/7 * 13 * 100

➜ volume of the tube = 22/7 * 1300

➜ volume of the tube = 28600/7 cm³

By formula of the density;

➜ density = weight/volume

➜ 7.8 = weight/(28600/7)

➜ weight/28600 = 7.8/7

➜ weight = (7.8/7) * 28600

➜ weight = 7.8 * 4085.7142

➜ weight = 31868.57076 gram or 31.86857076 kg

Answer : Hence, the weight of the metallic tube is 31868.57076 gram or 31.86857076 kg.