The sum of the inner and the outer curved surfaces of a hollow metallic cylinder is 1056 cm 2 and the volume of the material is 1056 cm 3 . Find its internal and external radii. Given that the height of the cylinder is 21 cm.

Given, Sum of the inner and the outer curved surfaces of a hollow metallic cylinder = 1056 cm 2 ∴ 2πrh + 2πRh = 1056 ⇒ 2πh(r + R) = 1056 ⇒ = 1056 ⇒ h(r + R) = ⇒ h(r + R) = 168 ...........(1) Volume of the material = 1056 cm 3 ∴ π(R 2 - r 2 )h = 1056 ⇒ = 1056 ⇒ (R 2 - r 2 )h = ⇒ (R 2 - r 2 )h = 336 .........(2) Dividing (2) by (1) we get, Substituting value of height and R in equation (1) we get : ⇒ 21(r + r + 2) = 168 ⇒ 21(2r + 2) = 168 ⇒ 2r + 2 = ⇒ 2r + 2 = 8 ⇒ 2r = 8 - 2 ⇒ 2r = 6 ⇒ r = ⇒ r = 3 cm. ⇒ R = r + 2 = 3 + 2 = 5 cm. Hence, internal radius = 3 cm and external radius = 5 cm.

Mathematics

The sum of the inner and the outer curved surfaces of a hollow metallic cylinder is 1056 cm² and the volume of the material is 1056 cm³. Find its internal and external radii. Given that the height of the cylinder is 21 cm.

Mensuration

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Mathematics

The sum of the inner and the outer curved surfaces of a hollow metallic cylinder is 1056 cm² and the volume of the material is 1056 cm³. Find its internal and external radii. Given that the height of the cylinder is 21 cm.

Mensuration

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Mathematics

The sum of the inner and the outer curved surfaces of a hollow metallic cylinder is 1056 cm2 and the volume of the material is 1056 cm3. Find its internal and external radii. Given that the height of the cylinder is 21 cm.

Mensuration

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