Question

plz solve it............. ​

Answer 1

Figure refers to the attachment :-

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★ 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.

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✒ The thickness of the cylinder is 0.368 cm.

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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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