the total surface area of hollow cylinder which is open from both sides is 4620square cm area of base ring is 115.5 square cm and height is 7 cm. find the thickness of cylinder
Answers
Step-by-step explanation:
Let the radii of outer and inner surfaces be R and r.
(I) TSA of hollow cylinder :
TSA = Outer CSA + Inner CSA + 2(Area of circular base)
➳ 4620 = 2πRh + 2πrh + 2π(R² - r²)
➳ 4620 = 2πh(R + r) + 2 × 115.5
➳ 4620 = 2πh(R + r) + 231
➳ 4620 - 231 = 2πh(R + r)
➳ 4389 = 2πh(R + r)
➳ 4389 = 2 × 22/7 × 7 × (R + r)
➳ 4389 = 44 × (R + r)
➳ 4389/44 = (R + r)
➳ 399/4 = (R + r) ...........[Equation (i)]
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(II) Area of base ring :
Area of base ring = π(R² - r²)
➳ 115.5 = 22/7(R² - r²)
➳ 115.5 × 7 = 22(R² - r²)
➳ 808.5/22 = R² - r²
➳ 8085/22 = R² - r²
➳ 147/4 = (R + r) (R - r).......[Equation (ii)]
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Now, Substituting equation (I) in equation (II) we get,
➳ 147/4 = (R + r) (R - r)
➳ 147/4 = (399/4) (R - r)
➳ (R - r) = 399/147
➳ (R - r) = 7/19
➳ (R - r) = 0.36842 cm
Therefore, the thickness of the cylinder is 0.36842 cm.
GivEn total surface area of hollow cylinder is 4620 cm²
Area of base ring is 115.5 cm².
Height of cylinder is 7 cm
We have to find, Thickness of cylinder.
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☯ So, Let's radius of outer surface be R.
☯ And, Radius of inner surface be r.
⋆ We have,
Area of base ring = 115.5 cm²
Therefore,
➟ Area of base ring = π(R² - r²)
⋆ Putting values,
➟ 115.5 = 22/7(R² - r²)
➟ 115.5 × 7/22 = R² - r²
➟ 808.5/22 = R² - r²
➟ 8085/220 = R² - r²
➟ 147/4 = (R + r)(R - r) .....[eq. (1)]
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★ Now we have to find TSA of hollow cylinder
➟ TSA = Outer CSA + Inner CSA + 2(Area of circular base)
➟ 4620 = 2πRh + 2πrh + 2(πR² - πr²)
➟ 4620 = 2πRh + 2πrh + 2π(R² - r)
⋆ Now, Putting values,
➟ 4620 = 2πh(R + r) + 2 × 115.5
➟ 4620 = 2πh(R + r) + 231
➟ 4620 - 231 = 2πh(R + r)
➟ 4389 = 2πh(R + r)
➟ 4389 = 2 × 22/7 × 7(R + r)
➟ 4389 = 2 × 22(R + r)
➟ 4389 = 44(R + r)
➟ 4389/44 = (R + r)
➟ 399/4 = (R + r) .....[eq. (2)]
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★ Now, Putting value of eq(2) in eq(1),
➟ 147/4 = (339/4)(R - r)
➟ 147/4 × 4/339 = (R - r)
➟ (R - r) = 147/339
➟ (R - r) = 7/19
Therefore,
➟ (R - r) = 0.36842 cm
⋆ We know that,
Thickness of cylinder = Outer radius - Inner Radius = (R - r)
∴ The Thickness of Cylinder is 0.36842 cm.