A triangle whose sides are 3cm, 4cm and 5cm is revolved about the sides containing 5cm.Find the volume of the solids so formed?
Answers
Answer:
volume of solid so formed is 60
volume of the solids so formed = 9.6π cm³ or 30 cm³
Step-by-step explanation:
Right angle triangle is revolved about the hypotenuse BC, the figure so formed is a double cone.
Attached is figure
In triangle ABC,
AB = 3 cm
AC = 4 cm
BC = 5 cm
OB = h₁
OC = h₂
OA = OD = r
h₁ + h₂ = 5
3² =h₁² + r²
4² = h₂² + r²
=> 4² - 3² = h₂² - h₁²
=> 16- 9 = (h₂+ h₁)(h₂ - h₁)
=> 7 = 5(h₂ - h₁)
=> h₂ - h₁ =7/5
h₁ + h₂ = 5
=> h₁ = 9/5
=> h₂ = 16/5
3² =h₁² + r² or 4² = h₂² + r²
=> r² = 9 - (81/25) or 16 - (256/25)
=> r² = 144/25
=> r = 12 /5
Total Volume = Volume of both cone
= (1/3)π (12/5)² * (9/5) + (1/3)π (12/5)² * (16/5)
= ( (1/3)π 144 / 5
= 48 π / 5
= 30 cm³
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