Question

Find the surface area of a flute made up of African Blackwood of diameter 1.4 cm and length 25 cm having 5 holes of 1.4 cm diameter.

• A. $1400{\text{cm}}^2$
• B. $700{\text{cm}}^2$
• C. $202.3{\text{cm}}^2$
• D. $102.3{\text{cm}}^2$

Answer 1

The correct option is D $102.3{\text{cm}}^2$

Given, Flute
Flutes are hollow cylindrical solids.
Length, $h=25\text{cm}$
Diameter of Flute $=1.4\text{cm}$
Radius of Flute, $r=\frac{1.4}{2}=0.7\text{cm}$
Number of Holes $=5$
Diameter of holes $=1.4\text{cm}$
Radius of holes, $R=\frac{1.4}{2}=0.7\text{cm}$

Surface area of Flute $=\text{CSA of Cylinder - Area of 5 holes}=2\pi rh-5\times \pi R^2=2\times \frac{22}{7}\times 0.7\times 25-5\times \frac{22}{7}\times 0.7\times 0.7=110-7.7=102.3{\text{cm}}^2$

$\therefore$ The Surface area of flute is $102.3{\text{cm}}^2$.