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The ratio of the radius and height of a cylinder is 2:3. If its volume is 12,936 cm³, find the total surface area of the cylinder.

Solution:

Volume of a cylinder = πr²h

Where r = radius

& h = height

Given that r/h = 2/3 we have

r = 2h/3

Volume = πr²h = π(2h/3)²(h) = 12,936

(4/9)πh³ = 12936

πh³ = 29,106

h³ = 29,106 × (7/22) = 1323 × 7 = 7 × 7 × 3 × 9 × 7 = 3³ × 7³

h = 21cm

r = 2 × 21/3 = 14 cm

The total Surface Area of a cylinder = 2πrh + 2πr² = 2πr(h + r) = 2 × (22/7) × (14 + 21) = 3080 cm²

✦ Try This: The ratio of the radius and height of a cylinder is 1:3. If its volume is 87,318 cm³, find the total surface area of the cylinder.

Volume of a cylinder = πr²h

Where r = radius

& h = height

Given that r/h = 1/3 we have

r = h/3

Volume = πr²h = π(h/3)²(h) = 87,318

(1/9)πh³ = 87,318

h³ = 87,318 × 7 × 9 × (1/22)

h³ = 3969 × 7 × 9

h³ = 3 × 1323 × 7 × 9

h³ = 3 × 3 × 441 × 7 × 3²

h³ = 3 × 3 × 21 × 21 × 7 × 3²

h³ = 3 × 3 × 3 × 7 × 3 × 7 × 7 × 3²

h³ = 3⁶ × 7³

h = 9 × 7 = 63cm

r = 63/3 = 21 cm

The total Surface Area of a cylinder = 2πrh = 2 × (22/7) × 21 × 63 = 8316 cm²

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

NCERT Exemplar Class 8 Maths Chapter 11 Problem 108

Summary:

The ratio of the radius and height of a cylinder is 2:3. If its volume is 12,936 cm³, the total surface area of the cylinder is 3080cm²

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