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Answer 1

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
• Jeight = 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.

=> (R - r)(R - r) = 115.5 × 7/22

=> 99.75(R - r) = 115.5 × 7/22

=> R - r = 7/19

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

Answer 2

Figure refers to the attachment

$\mathtt{\bf{\huge{\underline{\red{Question\:?}}}}}$

★ The total surface area of hollow cylinder, which is open from both sides, is 4620 cm²; area of the base ring is 115.5 cm² and height is 7 cm. Find the thickness of the cylinder.

$\mathtt{\bf{\huge{\underline{\green{Answer:-}}}}}$

✒ The thickness of the cylinder is 0.368 cm.

$\mathtt{\bf{\huge{\underline{\pink{Calcutaion:-}}}}}$

Given :-

• The total surface area of hollow cylinder, which is open from both sides, is 4620 cm²

• The area of the base ring is 115.5 cm².

• The height is 7 cm.

To Find :-

• The thickness of the cylinder.

Solution :-

Let the radius of outer surface be R

& the radius of inner surface are r .

∴ Area of the base ring = π(R² - r²)

➝ 115.5 = π(R² - r²)

➝ (R² - r²) = 115.5 ÷ 22/7

➝ (R² - r²) = $\dfrac{1155 × 7}{22}$

➝(R + r) (R - r) = $\dfrac{1155 × 7}{220}$

(R + r) (R - r) = $\dfrac{147}{4}$ cm²______{1}

According to the question,

• Total surface area of the cylinder = 4620 sq cm

★ We know that the total surface area of a hollow cylinder = (outer curved surface of cylinder + inner curved surface area of cylinder ) + 2( The circular base area of cylinder )

➝ 2πRh + 2πrh + 2π(R² - r²)

➝ 2πRh + 2πrh + 2π(R² - r²) = 4620

➝ 2πh (R + r) + (2 × 115.5) = 4620

➝ 2πh (R + r) + 231 = 4620

➝ 2πh (R + r) = 4620 - 231

➝ 2 × 22/7 × 7 × (R + r) = 4389

➝ (R + r) = $\dfrac{4389}{44}$

➝ (R + r) = $\dfrac{399}{4}$ __[2]

Putting value of 2 in equation (1)

➝ (R + r)(R - r) = $\dfrac{147}{4}$

➝ $\dfrac{399}{4}$(R - r) = $\dfrac{147}{4}$

➝(R - r) = $\dfrac{147}{4}$÷ $\dfrac{399}{4}$

➝ (R - r) = $\dfrac{147}{4}$× $\dfrac{4}{399}$

➝ (R - r) = $\dfrac{147}{399}$

➝ (R - r) = $\dfrac{7}{19}$ cm

➝ (R - r) = 0.368 cm

Therefore, the cylinder's thickness is 0.368 cm.

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Information Regarding Question :-

We have a cylinder with its dimensions, we have to find its thickness , by applying formulae of cylinder we have to find.

• Area of the base ring = π(R² - r²)

• The total surface area of a hollow cylinder = (outer curved surface of cylinder + inner curved surface area of cylinder ) + 2( The circular base area of cylinder )

Application :-

• In physics practical .
• Making sports goods.
• Used in Industries .
• Making bangles.
• Making coils.

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