Question

A solid cylinder has total sirface area of 462 sq cm. Its curved surface area is one ‐ third of its total surface area. Find the radius and height of the cylinder.​

Answer 1

Answer:

Step-by-step explanation:

We have Total Surface Area of cylinder

= 2πr( h + r ) or 2πrh + 2πr²

2πrh + 2πr² = 462 cm² _(i)

Where,

Curved Surface Area = ⅓ Total Surface Area

2πrh = ⅓ × 462 cm²

2πrh = 154 cm²

Substituting value of 2πrh in eq (i),

154 cm² + 2πr² = 462 cm²

2πr² = 462 - 154 cm² = 308 cm²

r² = 308/2π

r² = 308 × 1/2 × 7/22 cm²

r² = 28 × 1/2 × 7/2 cm²

r = √49 cm² = 7 cm

Substituting value of r in 2πrh

2πrh = 154 cm²

h = 154/2πr

h = 154 × 1/2 × 7/22 × 1/7 cm

h = 7/2 cm

Volume of cylinder = πr²h

= 22/7 × 7² × 7/2 cm³

= 539 cm³

hope it helps

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Answer 2

Given that:

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• Total surface area of the solid = 462 sq cm.
• Its curved surface area is one ‐ third of its total surface area.

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To find:

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Radius and height of the cylinder.

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Solution:

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We know that,

• Curved surface area = 2πrh and
• Total surface area = 2πrh + 2πr$^{2}$

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According to the question,

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Curved surface area = 1/3 × Total surface area

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$\implies$ 2πrh = 1/3 × (2πrh + 2πr$^{2}$)

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$\implies$ 4πrh = 2πr$^{2}$

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$\implies$ 2h = r

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Now, total suface area = 462(given)

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$\implies$ Curved surface area = 1/3 ×462

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$\implies$ 2πrh = 154

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$\implies$ 2 × 22/7 × 2h$^{2}$ = 154

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$\implies$ h$^{2} }/tex] </p><p>[tex] = \frac{154 \times 7}{2 \times 22 \times 2} = \frac{49}{4} \\ \\ = \frac{7}{2} \: cm$

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Height of the cylinder = 7/2 cm and radius of the cylinder = 2h = 2 × 7/2 = 7 cm.