Question

The ratio between the radius of the base and the height of the cylinder is 2: 3. If its volume is 1617 cm3, the total surface area of the cylinder is?

Answer 1

Solution:-

Given:-

• Ratio between the radius of the base and the height of the cylinder is 2: 3.
• volume is 1617 cm³.

To Find:-

• Total surface area of the cylinder = ?

Find:-

Let the radius of the base and the height of the cylinder be 2x and 3x respectively.

Now,

Volume of Cylinder = πr²h

=) 1617 = π× (2x)² × (3x)

=) 1617 × 7/22 = 4x² × 3x

=) 514.5 = 12x³

=) x³ = 514.5/12

=) x³ = 42.875

=) x = ³√( 42.875)

=) x = 3.5

Hence,

• Radius = 2x = 2×3.5 = 7 cm.
• Height = 3x = 3 × 3.5 = 10.5 cm.

Now,

Total Surface Area of Cylinder = 2πr ( h + r)

=) T.S.A. of Cylinder = 2 × (22/7) × 7 ( 10.5 + 7 )

=) T.S.A. of Cylinder = 44 ( 17.5 )

=) T.S.A. of Cylinder = 770 cm³.

Hence,

Total surface area of the cylinder is 770 cm³.