Volume & Surface Area: WJEC GCSE Higher November 2022 Unit 2 Q11

Higher November 2022 Unit 2 Q11

WJECHigherCurrent spec3 marksVolume & Surface Area

11. A cone is joined to a hemisphere, as shown below.
The cone has a base radius of 8 cm and a slant height of 17 cm.
The hemisphere has the same radius as the cone.
Calculate the surface area of the composite solid. [3]

Cone on top of a hemisphere, cone slant height 17 cm, common radius 8 cm

Diagram not drawn to scale

From the formula list: Surface area of sphere \(= 4\pi r^2\); Curved surface area of cone \(= \pi r l\)

Mark scheme

Scheme	Marks	Comments
(Curved surface area of cone + curved surface area of hemisphere =) \(\pi \times 8 \times 17\ +\ \dfrac{4 \times \pi \times 8^2}{2}\)	M2	May be seen in parts. If M2 not awarded, award M1 for any of the following: \(\pi \times 8 \times 17\) sight of 136π or a value between 427 and 427·312 \(4/2 \times \pi \times 8^2\) sight of 128π or a value between 401·9 and 402·2
(Total surface area =) Answer in the range 828·9 (cm²) to 829·512 (cm²) or 830 (cm²) or 264π (cm²)	A1	CAO Unsupported correct answer is awarded full marks.