Question

The perimeter and area of semicircular plate of radius 25cm are respectively (tale ∏=3.14)
A) 625.5cm, 981.25 \[c{m^2}\]
B) 128.5cm, 981.25 \[c{m^2}\]
C) 412.5cm, 981.25 \[c{m^2}\]
D) 188.5cm, 981.25 \[c{m^2}\]

Answer 1

Hint:
For a semicircle area is exactly half of a circular plate. But the perimeter is half of the perimeter of the circular plate with addition of length of diameter.
Formula used:
Perimeter of semicircular plate = \[\pi r + d\] or \[\pi r + 2r\]
Area of semicircular plate = \[\dfrac{{\pi {r^2}}}{2}\]

Complete step by step solution:
Given that the radius of the semicircular plate is 25cm.

Using the formulas above we will find the perimeter and area.
Perimeter of semicircular plate = \[\pi r + 2r\]
\[
   \Rightarrow 3.14 \times 25 + 2 \times 25 \\
   \Rightarrow 25\left( {3.14 + 2} \right) \\
   \Rightarrow 25\left( {5.14} \right) \\
   \Rightarrow 128.50cm \\
\]
If we observe the options there is no different option for the area. we can directly go for an option with the correct perimeter but we will find the area also.
Area of semicircular plate = \[\dfrac{{\pi {r^2}}}{2}\]
\[
   \Rightarrow \dfrac{{3.14 \times {{25}^2}}}{2} \\
   \Rightarrow \dfrac{{3.14 \times 625}}{2} \\
   \Rightarrow 981.25c{m^2} \\
\]
Thus we found the perimeter and area of that semicircular plate.

So the correct option is B.

Note:
Students generally calculate the perimeter of a semicircle as half of a circle but forget to add the diameter length with it. Since it is the perimeter of the shape sum of all its sides should be taken.