The thickness of a hollow metallic cylinder is 2 cm. It is 70 cm long with outer radius of 14 cm. Find the volume of the metal used in making the cylinder, assuming that it is open at both the ends. Also find its weight if the metal weighs 8 g per cm³.

Solution:

The outer radius of the cylinder = 14cm

Inner radius = 14 - 2 = 12cm

Outer Volume = πR²h = π(14)²(70) = π(196)(70) cm³

Inner Volume = πr²h = π(12)²(70) = π(144)(70) cm³

The volume of metal used is given by the relation,

Outer Volume - Inner Volume = 70π(196 - 144) = 70π × 52 = (70) × (22/7) × 52 = 11440 cm³

The weight of the cylinder = 8 × (Outer Volume - Inner Volume)

The weight of the cylinder = 8 × 11440 = 91,520 g or 91.520 kgs

✦ Try This: The thickness of a hollow metallic cylinder is 2 cm. It is 140 cm long with outer radius of 7 cm. Find the volume of the metal used in making the cylinder, assuming that it is open at both the ends. Also find its weight if the metal weighs 6 g per cm³.

The outer radius of the cylinder = 7cm

Inner radius = 7 - 2 = 5 cm

Outer Volume = πR²h = π(7)²(140) = π(49)(140) cm³

Inner Volume = πr²h = π(5)²(140) = π(25)(140) cm³

The volume of metal used is given by the relation,

Outer Volume - Inner Volume = 140π(49 - 25) = 140π × 24 = (140) × (22/7) × 24 = 10,560 cm³

The weight of the cylinder = 8 × (Outer Volume - Inner Volume)

The weight of the cylinder = 8 × 10,560 = 84,480g or 84.480 kgs

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

NCERT Exemplar Class 8 Maths Chapter 11 Problem 91

The thickness of a hollow metallic cylinder is 2 cm. It is 70 cm long with outer radius of 14 cm. Find the volume of the metal used in making the cylinder, assuming that it is open at both the ends. Also find its weight if the metal weighs 8 g per cm³.

Summary:

The thickness of a hollow metallic cylinder is 2 cm. It is 70 cm long with outer radius of 14 cm. The volume of the metal used in making the cylinder, assuming that it is open at both the ends is 11440 cm³.Its weight if the metal weighs 8 g per cm³ 91.52 kgs

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