Question

The ratio between the radius and height of a cylinder is 2 : 3. If it's Volume is 12936cm³. Find the Total surface area of the cylinder. ​

Answer 1

Answer:

the answer is 6,947,977.14

Answer 2

Given:-

Ratio between the radius and height of a cylinder = 2 : 3

Volume = 12,936 cm³

To find:-

• Total Surface area of Cylinder

Solution:-

Let the radius of a cylinder be = 2x

Let the height of a cylinder be = 3x

As we know,

Volume of a cylinder = π r² h

⟹ 12936 = π (2x)² (3x)

⟹ 12936 = (${\frac{22}{7}}$) (4x²) (3x)

⟹ 12936 × 7 = 22 (12x³)

⟹ 90552 = 22 (12x³)

⟹ ${\cancel\frac{90552}{22}}$ = 12x³

⟹ 4116 = 12x³

⟹ ${\cancel \frac{4116}{12}}$ = x³

⟹ 343 = x³

⟹ x = 7

Now let us put the value of x,

Radius of a cylinder = 2x = 2(7) = 14 cm

Height of a cylinder = 3x = 3(7) = 21 cm

Finally, let us find Total Surface Area:

Total Surface Area of the cylinder

=2 π r (r + h)

= 2(${\frac{22}{7}}$) 14(14 +21)

= ${\frac{44}{7}}$ × 14 (35)

= ${\frac{44}{7}}$ × 490

= 44 × 70

= 3080 cm²

★ Required Answer:-

Total Surface Area of the cylinder = 3080 cm²