Question

The total surface area of a hollow 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.
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Answer 1

Answer:

Area of the base ring = π(R² - r²)⇒ 115.5 = π(R² - r²)⇒ (R² - r²) = 115.5 ÷ 22 /7(… ... Find the thickness of the cylinder. ... Total surface area of the cylinder = 4620....

Answer 2

Given:-

• The total surface area of a hollow cylinder which is open from both sides is 4620 sq. cm,
• area of base ring is 115.5 sq. cm and height 7 cm.

To find:-

• Find the thickness of the cylinder.

Solutions:-

The cylinder is a hollow cylinder and is open on both sides.

Total surface area of the cylinder is 4620cm²

Area of the base ring = 115.5cm²

height = 7cm

Total surface area of a hollow cylinder

= 2πrh + 2πRh + 2πR² - 2πr²

where, r is the inner radius and R is the outer radius of the cylinder.

Now,

2πrh + 2πRh + 2πR² - 2πr² = 4620

Also, h = 7cm

2πh(r + R) + 2(πR² - πr²) = 4620

Area of base ring = 115.5

(πR² - πr²) = 115.5

π(R² - r²) = 115.5 ...................(i).

Substituting for πR² - πr² in the above equation, we have.

2πh(r + R) + 2(115.5) = 4620

2πh(r + R) + 231 = 4620

2πh(r + R) = 4620 - 231

2πh(r + R) = 4389

Also, h = 7cm

Therefore,

2πh(r + R) = 4389

2 × 22/7 × 7 (r + R) = 4389

44(r + R) = 4389

r + R = 4389/44

r + R = 99.75 ....................(ii).

Now, let us again take up Eq. (i).

π(R² - r²) = 115.5

[22(R² - r²)]/7 = 115.5

(R² - r²) = 115.5 × 7/22

(R - r)(R - r) = 115.5 × 7/22

from Eq. (ii) we have R + r = 99.75

substitute In the above equation.

99.75(R - r) = 115.5 × 7/22

R - r = 7/19

Hence, the thickness of the cylinder is 7/19 cm.