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J asked in Science & MathematicsMathematics · 2 months ago

Hello I need help with these questions. Thank you.?

8 Modelling / Problem-solving Kathy makes cakes for special events.

She uses a cake tin with a 20 cm diameter.

Kathy puts ribbon around each cake.

She allows an extra 2 cm of ribbon for joining.

a) How much ribbon does she need for each cake?

b) She buys the ribbon in rolls of 25 metres.

How many cakes can she decorate from one roll?

9) Modelling / Problem-solving Peter is putting edging round a circular

flower bed with diameter 460 cm.

The edging comes in 245 cm lengths. How many lengths does he need?

10) The radius of a racing bike wheel is 340 mm.

How many revolutions will the wheel make in a 500 m

sprint race?

1 Answer

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  • 2 months ago

    The circumference of the cake is:

    c = π.d → where d is the diameter of the cake

    c = 20π → but you need 2 cm more

    c = 20π + 2

    She buys the ribbon in rolls of 25 m. The number of cakes is:

    n = ℓ/c → where ℓ is the length of the ribbon in cm, i.e. 2500

    n = 2500/(20π + 2)

    n = 2500/[2.(10π + 1)]

    n = 1250/(10π + 1)

    n ≈ 38.56 → as n is an integer

    n = 38

    Peter is putting edging round a circular flower bed with diameter 460 cm.

    The circumference is:

    c = π.d → where d is the diameter of the bed

    c = 460π

    The number of lengths is:

    n = c/245

    n = 460π/245

    n = 92π/49

    n ≈ 5.89 → as n is an integer

    n = 6

    The radius of the wheel is 340 mm. The circumference is:

    c = π.d → where d is the diameter of the wheel, here: 2 * 340 = 680 mm

    c = 680π

    The number of revolutions for 500 m (i.e. 500000 mm) is:

    n = 500000/c

    n = 500000/(680π)

    n = 12500/(17π)

    n ≈ 234.05 → as n is an integer

    n = 235

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