Unit 17 Perimeter, area and volume 2 5 a Estimate the area of each of these circular objects. i The head of a nail with a radius of 3 mm. ii A trampoline with a diameter of 14 feet. iii The Caldera Crater at Yellowstone Lake with a diameter of 5 km. b Calculate each area in part a leaving your answers in terms of p. c Calculate each area in part a correct to 2 s.f. 6 Q5a i hint p × 32 = 9p ≈ 9 × Reasoning Rita says the area of the circle is 25p cm2. Jack says the area of the circle is 100p cm2. Who is correct? Explain your answer. 10 cm 7 Real A circular space has a radius of 4.5 m. a Work out the area of the space. b To make a lawn Grace sows 50 g of grass seed per m2. How much grass seed does Grace need to cover this space? 8 STEM / Modelling A scientist wants to estimate the number of slugs in a field with an area of 4050 m2. She uses a piece of string to mark out a circle with a radius of 1.5 m. a Work out the area of the circle. b She finds 35 slugs inside the circle. Estimate the number of slugs in the field. Discussion How reliable is your estimate? Example 3 The area of a circle is 98.5 cm2. Work out the radius of the circle. Give your answer correct to 1 d.p. A = π r 2 98.5 = πr 2 _____ 98.5 = r 2 π _____ √ _____ 98.5 = r π Show the substitution. Make r2 the subject. Square root both sides. r = 5.599 421 737 r = 5.6 cm (to 1 d.p.) 9 For each circle work out i the radius ii the diameter. a A = 124.7 m2 Write down all the figures on the calculator display. Round the answer to the required accuracy. Remember the units. b c A = 13.8 cm2 10 Modelling A sprinkler covers a circular area of 380 m2. How far from the sprinkler head does the water reach? Give your answer to an appropriate degree of accuracy. 510 A = 1.44p cm2 Q10 hint Sketch a diagram.