Question

Find curved surface area and total surface area of cylinder whose volume is 1.54 m cube and radius of base is 70 cm​

Answer 1

Given:-

• Volume of cylinder = 1.54 m³.
• Radius of base = 70 cm = 0.7m.

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To find:-

• Curved surface area and total surface area of cylinder?

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Solution:-

★ Formula used:-

$\star{\boxed{\sf{\orange{Volume\: of\: cylinder = \pi r^2h}}}}$

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$\large{\tt{\longmapsto{1.54 = \pi (0.7)^2h}}}$

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$\large{\tt{\longmapsto{1.54 = \dfrac{22}{7} \times 0.49 \times h}}}$

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$\large{\tt{\longmapsto{1.54 = 22 \times 0.7 \times h}}}$

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$\large{\tt{\longmapsto{1.54 = 15.4h}}}$

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$\large{\tt{\longmapsto{h = \dfrac{1.54}{15.4}}}}$

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$\large{\tt{\longmapsto{h = 0.1}}}$

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• Height = 0.1 m

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$\boxed{\sf{\orange{TSA = 2 \pi r(h + r)}}}$

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$\large{\tt{\longmapsto{TSA = 2 \times \dfrac{22}{7} \times 0.7 (0.1 + 0.7)}}}$

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$\large{\tt{\longmapsto{TSA = 44 \times 0.1(0.8)}}}$

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$\large{\tt{\longmapsto{TSA = 44 \times 0.08}}}$

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$\large{\tt{\longmapsto{TSA = 3.52}}}$

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• Total surface area of Cylinder is 3.52m².

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$\boxed{\sf{\orange{CSA = 2 \pi rh}}}$

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$\large{\tt{\longmapsto{CSA = 2 \dfrac{22}{7} \times 0.7 \times 0.1}}}$

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$\large{\tt{\longmapsto{CSA = 44 \times 0.1 \times 0.1}}}$

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$\large{\tt{\longmapsto{CSA = 44 \times 0.01}}}$

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$\large{\tt{\longmapsto{CSA = 0.44}}}$

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• Curved surface area of Cylinder is 0.44 m².

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Hence, total surface area of the cylinder is 3.52m² and the curved surface area of Cylinder is 0.44m².

Answer 2

Given:-

• Volume of cylinder = 1.54 m³.
• Radius of base = 70 cm = 0.7m.

⠀

To find:-

• Curved surface area and total surface area of cylinder?

⠀

Solution:-

★ Formula used:-

$\star{\boxed{\sf{\orange{Volume\: of\: cylinder = \pi r^2h}}}}$

⠀

$\large{\tt{\longmapsto{1.54 = \pi (0.7)^2h}}}$

⠀

$\large{\tt{\longmapsto{1.54 = \dfrac{22}{7} \times 0.49 \times h}}}$

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$\large{\tt{\longmapsto{1.54 = 22 \times 0.7 \times h}}}$

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$\large{\tt{\longmapsto{1.54 = 15.4h}}}$

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$\large{\tt{\longmapsto{h = \dfrac{1.54}{15.4}}}}$

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$\large{\tt{\longmapsto{h = 0.1}}}$

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Height = 0.1 m

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$\boxed{\sf{\orange{TSA = 2 \pi r(h + r)}}}$

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$\large{\tt{\longmapsto{TSA = 2 \times \dfrac{22}{7} \times 0.7 (0.1 + 0.7)}}}$

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$\large{\tt{\longmapsto{TSA = 44 \times 0.1(0.8)}}}$

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$\large{\tt{\longmapsto{TSA = 44 \times 0.08}}}$

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$\large{\tt{\longmapsto{TSA = 3.52}}}$

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Total surface area of Cylinder is 3.52m².

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$\boxed{\sf{\orange{CSA = 2 \pi rh}}}$

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$\large{\tt{\longmapsto{CSA = 2 \dfrac{22}{7} \times 0.7 \times 0.1}}}$

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$\large{\tt{\longmapsto{CSA = 44 \times 0.1 \times 0.1}}}$

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$\large{\tt{\longmapsto{CSA = 44 \times 0.01}}}$

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$\large{\tt{\longmapsto{CSA = 0.44}}}$

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Curved surface area of Cylinder is 0.44 m².

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Hence, total surface area of the cylinder is 3.52m² and the curved surface area of Cylinder is 0.44m².