Question

10. The radius and height of a cylinder are in the ratio 7: 2. If the volume of the cylinder is
8316 cm, find the total surface area of the cylinder.
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Answer 1

Answer:

Explanation:

Given :

• The radius and height of a cylinder are in the ratio 7: 2.
• Volume of the cylinder is 8316 cm³.

To Find :

• Total surface area of the cylinder.

Formula to be used :

• Volume = πr²h
• TSA = 2πr(r + h)

Solution :

Given, The radius and height of a cylinder are in the ratio 7: 2.

⇒ r/h = 7/2

⇒ h = 2r/7

Volume of the cylinder = πr²h

⇒ 8316 = 22/7 × r² × (2r/7)

⇒ 8316 = 22/7 × 2r³/7

⇒ 8316 = 22/7 × 2 × r³/7

⇒ r³ = 8316 × 7 × 7 / 2 × 22

⇒ r³ = 7³ × 3³

⇒ r = 7 × 3

⇒ r = 21 cm

.°. h = 2r/7 ⇒ 2 × 21/7 ⇒ 42/7 ⇒6 cm

TSA of the cylinder = 2πr(r + h)

⇒ TSA = 2 × 22/7 × 21(21 + 6)

⇒ TSA = 44 × 3(27)

⇒ TSA = 132(27)

⇒ TSA = 3564 cm²

Hence, Total surface area of the cylinder is 3564 cm².

Answer 2

Answer:

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