The total surface area of ahollow cylinder which is open from both sides is 4620 sq. cm, area of base ring is 115.5 sq. cm and height 7 cm. Find the thickness of the cylinder.
Answers
The thickness of the hollow cylinder is 0.358 cm.
• Given,
Total surface area of the hollow cylinder (T.S.A) = 4620 sq. cm
Area of the base ring = 115.5 sq. cm
Height of the cylinder (h) = 7 cm
• Total surface area of a hollow cylinder (T.S.A.) = Outer curved surface area of the cylinder + Inner curved surface area of the cylinder + Area of the base ring
• Let the radius of the outer cylinder be R cm, and that of the inner cylinder be r cm.
• Now,
Outer curved surface area of the cylinder = 2πRh
Inner curved surface area of the cylinder = 2πrh
Area of the base ring = Area of outer cylinder - Area of inner cylinder
=> Area of base ring = πR² - πr²
=> 115.5 sq. cm = π (R² - r²)
=> 115.5 sq. cm = π (R - r) (R + r)
[ Applying a² - b² = (a - b) (a + b) ]
• Therefore,
T.S.A. = 2πRh + 2πrh + π (R - r) (R + r)
Or, 4620 sq. cm = 2πh (R + r) + 115.5 sq. cm
Or, 2πh (R + r) = 4620 sq. cm - 115.5 sq. cm
Or, 2 × (22 / 7) × 7 cm × (R + r) = 4504.5 sq. cm
Or, 2 × 22 cm × (R + r) = 4504.5 sq. cm
Or, 44 cm × (R + r) = 4504.5 sq. cm
Or, R + r = 4504.5 sq. cm / 44 cm
Or, R + r = 102.375 cm
• Thickness of a hollow cylinder = Outer Radius - Inner Radius
=> Thickness of the hollow cylinder = R - r
• Putting the value of (R + r) in eq. (i), we get,
115.5 sq. cm = π (R - r) × 102.375 cm
Or, π (R - r) = 115.5 sq. cm / 102.375 cm
Or, (22 / 7) (R - r) = 1.128 cm
Or, R - r = (1.128 cm × 7) / 22
Or, R - r = 7.817 cm / 22
Or, R - r = 0.358 cm
∴ Thickness of the hollow cylinder = 0.358 cm.
Answer:
Step-by-step explanation:• Given,
Total surface area of the hollow cylinder (T.S.A) = 4620 sq. cm
Area of the base ring = 115.5 sq. cm
Height of the cylinder (h) = 7 cm
• Total surface area of a hollow cylinder (T.S.A.) = Outer curved surface area of the cylinder + Inner curved surface area of the cylinder + Area of the base ring
• Let the radius of the outer cylinder be R cm, and that of the inner cylinder be r cm.
• Now,
Outer curved surface area of the cylinder = 2πRh
Inner curved surface area of the cylinder = 2πrh
Area of the base ring = Area of outer cylinder - Area of inner cylinder
=> Area of base ring = πR² - πr²
=> 115.5 sq. cm = π (R² - r²)
=> 115.5 sq. cm = π (R - r) (R + r)
[ Applying a² - b² = (a - b) (a + b) ]
• Therefore,
T.S.A. = 2πRh + 2πrh + π (R - r) (R + r)
Or, 4620 sq. cm = 2πh (R + r) + 115.5 sq. cm
Or, 2πh (R + r) = 4620 sq. cm - 115.5 sq. cm
Or, 2 × (22 / 7) × 7 cm × (R + r) = 4504.5 sq. cm
Or, 2 × 22 cm × (R + r) = 4504.5 sq. cm
Or, 44 cm × (R + r) = 4504.5 sq. cm
Or, R + r = 4504.5 sq. cm / 44 cm
Or, R + r = 102.375 cm
• Thickness of a hollow cylinder = Outer Radius - Inner Radius
=> Thickness of the hollow cylinder = R - r
• Putting the value of (R + r) in eq. (i), we get,
115.5 sq. cm = π (R - r) × 102.375 cm
Or, π (R - r) = 115.5 sq. cm / 102.375 cm
Or, (22 / 7) (R - r) = 1.128 cm
Or, R - r = (1.128 cm × 7) / 22
Or, R - r = 7.817 cm / 22
Or, R - r = 0.358 cm
∴ Thickness of the hollow cylinder = 0.358 cm