The diagram shows two quarter
circles with radii three meters. Calculate the total area of the
shape. Give your answer in terms of
To find the area of a full circle,
we can use the formula 𝜋𝑟 squared, where 𝑟 represents the radius of the
circle. But we’re told that the diagram
consists of two quarter circles. So to find the area of each quarter
circle, we’d need to divide 𝜋𝑟 squared by four. We could then multiply this by two
as we have two quarter circles.
Or another way to approach this
would be to think that if we put two quarter circles together, then they form a
semicircle. So rather than finding the area of
each quarter circle and doubling it, we could instead just find the area of a
semicircle by dividing our formula 𝜋𝑟 squared by two.
In this question, we’re told that
the radii of the quarter circles and therefore the radius of the full circle is
three meters. So substituting this value for 𝑟
into our formula for the area of the semicircle gives 𝜋 multiplied by three squared
Three squared just means three
multiplied by three which is nine and 𝜋 multiplied by nine can be written as nine
𝜋. So the area simplifies to nine 𝜋
over two. We could also write this as nine
over two 𝜋 if we wish.
If we had access to a calculator,
then we could evaluate what nine over two times 𝜋 is equal to as a decimal. But this question asks us to give
our answer in terms of 𝜋. So we’ll leave our answer as nine
over two 𝜋.
As the units for the radius were
meters, the units for the area will be meters squared. So our answer is nine over two 𝜋