Area of circles
Calculate the area of circles using , given the radius or diameter, and find the area of semicircles and quarter-circles.
Worked examples
Finding the area of a circle given its radius
Straightforward
Problem
Find the area of a circle with radius cm. Give your answer correct to 2 decimal places.
1
Write the formula for the area of a circle.
2
Substitute .
3
Calculate to 2 decimal places.
cm²
Answer
cm²
Finding the area of a circle given its diameter
Moderate
Problem
Find the area of a circle with diameter cm. Give your answer correct to 2 decimal places.
1
Find the radius from the diameter.
cm
2
Write the formula and substitute .
3
Calculate to 2 decimal places.
cm²
Answer
cm²
Finding the area of a semicircle
Challenging
Problem
Find the area of a semicircle with diameter cm. Give your answer correct to 2 decimal places.
1
Find the radius from the diameter.
cm
2
Find the area of the full circle.
3
A semicircle is half a full circle.
4
Calculate to 2 decimal places.
cm²
Answer
cm²
Practise
Q1·Straightforward
Find the area of a circle with radius cm. Give your answer correct to 2 decimal places.
Explanation
cm²
Q2·Straightforward
Find the area of a circle with radius m. Give your answer correct to 2 decimal places.
Explanation
m²
Q3·Straightforward
Find the area of a circle with radius cm. Give your answer correct to 2 decimal places.
Explanation
cm²
Q4·Straightforward
A circle has radius mm. Find its area correct to 2 decimal places.
Explanation
mm²
Q5·Moderate
Find the area of a circle with diameter cm. Give your answer correct to 2 decimal places.
Explanation
cm; cm²
Q6·Moderate
A circle has a diameter of m. Find its area correct to 2 decimal places.
Explanation
m; m²
Q7·Moderate
The area of a circle is cm². Find the radius (in cm).
Explanation
cm
Q8·Moderate
The area of a circle is mm². Find the radius (in mm).
Explanation
mm
Q9·Challenging
Find the area of a semicircle with radius cm. Give your answer correct to 2 decimal places.
Explanation
Full circle: . Semicircle: cm²
Q10·Challenging
Find the area of a quarter-circle with radius m. Give your answer correct to 2 decimal places.
Explanation
Full circle: . Quarter-circle: m²
Q11·Challenging
A large circle has radius cm and a small circle has radius cm. Find the difference in their areas, correct to 2 decimal places.
Explanation
Large: . Small: . Difference: cm²
Q12·Challenging
Find the area of a semicircle with diameter mm. Give your answer correct to 2 decimal places.
Explanation
mm. Full circle: . Semicircle: mm²