Question

Find the area of annulus whose inner and outer radii are 6cm and 8cm.

Answer 1

Hint: We will use the area of the annulus, $\pi \left( {{R^2} - {r^2}} \right)$ where $R$ is the outer radii and $r$ is the inner radii to find the required area. We will substitute the value of inner and outer radii and then simplify it to get the required answer.

Complete step-by-step answer:
We have to find the area of the annulus whose inner and outer radii are 6cm and 8cm.
We know that the area of the annulus is $\pi \left( {{R^2} - {r^2}} \right)$, where $R$ is the outer radii and $r$ is the inner radii.

We will substitute the values of inner radii and outer radii in the above formula,
$\pi \left( {{{\left( 8 \right)}^2} - {{\left( 6 \right)}^2}} \right)$
We will simplify the above expression using the formula, ${a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)$
$
  \pi \left( {8 + 6} \right)\left( {8 - 6} \right) \\
   \Rightarrow \pi \left( {14} \right)\left( 2 \right) \\
$
On substituting the value of the $\pi = \dfrac{{22}}{7}$ in the above expression, we will get,
$
  \pi \left( {14} \right)\left( 2 \right) \\
   \Rightarrow \dfrac{{22}}{7}\left( {14} \right)\left( 2 \right) \\
   \Rightarrow 22\left( 4 \right) \\
   \Rightarrow 88c{m^2} \\
$
Hence, the area of the annulus is $88c{m^2}$.

Note: We can also do this question by finding the area of the outer circle and the inner circle and then we can subtract the area of the inner circle from the area of the outer circle.
The annulus is the part between the two circles.
Also, the area of any shape is measured in square units.