Question

A rectangular plate is of 6m breadth and 12 m length. Two apertures of 2 m diameter each and one aperture of 1 m diameter have been made with the help of a gas cutter. What is the area of the remaining portion of the plate?

• A. 68.5 sq.m
• B. 62.5 sq.m
• C. 65 sq.m
• D. None of these

Answer 1

The correct option is C 65 sq.m

Given, Length = 12m and Breadth = 6m
$\therefore$ Area of rectangular plate $=12\times 6=72m^2$

Since, two apertures of 2 m diameter each have been made from this plate.
$\therefore$ Area of these two apertures $=\pi (1{)}^2+\pi (1{)}^2$
$=\pi +\pi =2\pi$
Area of 1 aperture of 1m diameter $=\pi {\left(\frac{1}{2}\right)}^2=\frac{\pi }{4}$
$\therefore$ Total area of aperature $=2\pi +\frac{\pi }{4}=\frac{9\pi }{4}=\frac{9}{4}\times \frac{22}{7}=\frac{99}{14}$
$\therefore$ Area of the remaining portion of the plate
$=72-\frac{99}{14}sq.m=\frac{909}{14}sq.m\approx 65sq.m$