Question

The length of flute is 24cm and its diameter is 1.5cm. There are a total of 9 small circular cut outs. The diameter of each small circle is 0.5cm. The flute need to be painted from outside. Find the area of the flute that need to be painted​

Answer 1

Given,

The length of the flute is 24 cm.

The diameter of the flute is 1.5 cm.

Diameter of smaller holes is 0.5 cm.

Number of smaller holes is 9.

To find,

The area of the flute that is needed to be painted.

Solution,

Radius of the flute = 1.5/2 = 0.75 cm

Radius of the smaller hole = 0.5/2 = 0.25 cm

Curved surface area of the flute (including holes) = 2×π×0.75×24 = 2 × 22/7 × 0.75 × 24 = 113.14 cm²

Area of one hole = π × (0.25)² = 0.196 cm²

Area of 9 holes = 0.196×9 = 1.764 cm²

Total area for painting = (113.14-1.764) = 111.376 cm²

Hence, area for painting is 111.376 cm².