Question

14. The radius and height of a cylinder are in
the ratio 7:2. If the volume of the
cylinder is 6062364 cm3. Find the total
surface area of the cylinder?
​

Answer 1

Given:

✭ Radius and height are in the ratio 7:2

✭ Volume of the cylinder = 6062364 cm³

To Find:

◈ Total surface area of the cylinder?

Solution:

Let

• The radius of the cylinder be 7x cm
• The height of the cylinder be 2x cm

The volume of the cylinder is given by,

π r²h

• Volume = 6062364

➝ π r²h = 6062364

➝ 22/7 × 7x² × 2x = 6062364

➝ 22/7 × 7x × 7x × 2x = 6062364

➝ 22 × x × 7x × 2x = 6062364

➝ 308 x³ = 6062364

➝ x³ = 6062364/308

➝ x³ = 19683

➝ x = ∛19683

➝ x = 27

Hence,

Height of the cylinder = 2x

»» 2 × 27

»» Height of the cylinder = 54 cm

Radius of the cylinder = 7x

›› 7 × 27

›› Radius of the cylinder = 189

The total surface area of cylinder is given by,

πr(r + h)

Substituting the values,

➳ 3.14 × 54 (54 + 189)

➳ 41203.08 cm²

∴ CSA of the cylinder is 41203.08 cm²

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