Circles & Sectors: WJEC GCSE Numeracy Higher November 2017 Unit 2 Q8

Numeracy Higher November 2017 Unit 2 Q8

WJECHigherCurrent spec7 marksCircles & Sectors Pythagoras

8. A baker makes cake slices to sell in her shop.
All of the cake slices are identical. They have been cut from a cylindrical cake of radius 10 cm and depth 4 cm.

Piped icing is placed on the curved surface of each cake slice, as shown in the diagram.
It connects opposite vertices of this curved surface, and follows the shortest path between these vertices.

Cake slice: a sector-shaped prism with angle 20° at the centre, radius 10 cm and depth 4 cm; the piped icing runs across the curved face between opposite vertices

Diagram not drawn to scale

What length of piped icing will be needed to decorate all the slices that make up a whole cylindrical cake? [7]

Length of piped icing needed for a whole cake = …………… cm

Mark scheme

Scheme	Marks	Comments
(Length of circular arc =) \(\dfrac{20}{360}\) × 2 × π × 10	M1	Or equivalent
= 3∙48(888…) to 3∙5 (cm)	A1	(OR 10π/9 or equivalent)
(Length² =) 4² + (3∙48(888…) to 3∙5)²	M1	FT ‘their derived 3·48…’
Length² = 28·1104 to 28·25 or (Length =) √(28·1104 to 28·25)	A1
(Length =) 5·3 to 5·32 (cm)	A1	FT the square root of 'their 28·…' provided their answer is the longest length of their triangle. On FT, accept an answer that is correct to 1dp for ‘their 3∙48(888…)’.
(Total length of piping needed =) \(\dfrac{360}{20}\) × (5·3 to 5·32)	M1	FT ‘their 5·3…’ provided previous M1 awarded.
= 95·4 to 95·8 (cm)	A1