A fiction clutch is in the form of a frustum of a cone, the diameters of the ends being 32cm and 20cm.find it's bearing surface and volume
Answers
Step-by-step explanation:
Let, ABB'A' be the fiction lutch of slant height l cm.
Radius = diameter/2 ( half of diameter... )
Given, The diameter of the ends d₁ = 32 cm
d₂ = 20 cm
Length = 8 cm
( radius ) r₁ = 16 cm ( 32/2 )
r₂ = 10 cm ( 20/2 )
h = 8 cm
∴ l² = h² + ( r₁ - r₂ ) ²
⇒ l² = 64 + 36 => 100 cm²
l = 10 cm
Now after that ,
Bearing surface of the clutch = Lateral surface of the Frustum
= π ( r₁ + r₂ ) l
= 22/7 × ( 16 + 10 ) × 10 cm²
= 817.14 cm²
Volume = 1/3πh ( r₁² + r₁r₂ + r₂² )
→ Volume = 1/3 × 22/7 × 8 × ( 16² + 16 ×10 + 10² ) cm³
→ Volume = 1/3 × 22/7 × 8 × ( 256 + 160 + 100 ) cm³
→ Volume = 176/21 × 516 cm³