Question

The ratio of the radius to the height of a cylinder is 1:2 and sum of their lengths is42 cm. Find the total surface area of the cylinder.​

Answer 1

Given

• The ratio of the radius to the height of a cylinder is 1:2 and sum of their lengths is 42cm.

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To find

• Total surface area of the cylinder.

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Solution

• Let the ratio be x.

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❍ Radius = x

❍ Height = 2x

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{Sum\: of\: their\: lengths\: is\: 42cm}}}$

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→ x + 2x = 42

→ 3x = 42

→ x = 42/3

→ x = 14

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\green{By\: putting\: the\: value\: of\: x}}}$

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• Radius = 14cm
• Height = 28cm

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★Surface area = 2πr(h + r)

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⟹ Surface area = $\sf{2 \times \dfrac{22}{7} \times 14 (28 + 14)}$

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⟹ Surface area = 44 × 2 × 42

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⟹ Surface area = 88 × 42

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⟹ Surface area = 3,696 cm²

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Hence,

• The surface area of the cylinder is 3,696cm².

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