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15.3 Solving circle problems

15.3 Solving circle problems

When you used the formulae for the circumference and area of a circle, you took the value of π as 3.14.
Every scienti$c calculator has a ‘π’ button. !e value given by the ‘π’ button on a calculator is more
accurate than 3.14. Try it out. What do you notice? Using the ‘π’ button will give a more accurate answer.
When you solve circle problems, use the ‘π’ button on your calculator and make sure you use the
correct formulae for circumference and area.

Circumference: C = πd or C = 2πr
Area: A = πr 2

Worked example 15.3

Use the ‘π’ button on the calculator. Give all answers correct to one decimal place (1 d.p.).
a Work out the area and circumference of a circle with diameter 6.8 cm.
b Work out the area and perimeter of a semicircle with radius 7 m.
c A circle has circumference 12 mm. What is the diameter of the circle?
d A circle has area 24 cm . What is the radius of the circle?
2
a r = 6.8 ÷ 2 = 3.4 cm Divide the diameter by 2 to work out the radius.
A = πr = π × 3.4 Write down the formula for the area and substitute the value for r.
2
2
= 36.3 cm (1 d.p.) Write the answer correct to one decimal place.
2
C = πd = π × 6.8 Write down the formula for the circumference and substitute the value for d.
= 21.4 cm (1 d.p.) Write the answer correct to one decimal place.
b It is often helpful to draw a diagram to help you answer the question.
In this case, draw a semicircle and mark on the radius 7 m.
7 m
Area = π r 2 The area of a semicircle is half the area of a circle. Write down the
2
formula,
= π ×7 2 then substitute in the value for r.
2
= 77.0 m (1 d.p.) Write the answer correct to one decimal place.
2
Perimeter = 2πr + 2r The perimeter of a semicircle is half the circumference of the circle plus the
2
π
= 2×× 7 + × diameter of the circle. Write down the formula and substitute the value
27
2
for r. Write the answer correct to one decimal place.
= 36.0 m (1 d.p.)
c C = πd, so 12 = π × d Write down the formula for the circumference and substitute the value for C.
d = 12 Rearrange the equation to make d the subject, then work out the answer.
π
= 3.8 mm (1 d.p.) Write the answer correct to one decimal place.

d A = πr , so 24 = π × r Write down the formula for the area and substitute the value for A.
2
2
r = 24 Rearrange the equation to make r the subject, then work out the value
2
2
π
of r .
2
r = 7.639 437 268 Write down the full value of r . You must only round the final value for r.
2
2
r = 7 639 437 268. Rearrange the equation to make r the subject, then work out the answer.
r = 2.8 cm (1 d.p.) Write the final answer correct to one decimal place.
15 Area, perimeter and volume 145