Volume & Surface Area: WJEC GCSE Numeracy Higher June 2025 Unit 2 Q1

Numeracy Higher June 2025 Unit 2 Q1

WJECHigherCurrent spec3 marksVolume & Surface Area

1. Nina sells flowers.

She wants to display her flowers.
She buys two glass vases from a website.
The two vases are different shapes.

Diagrams not drawn to scale

Each vase can hold 1648 cm\(^3\) of water when it is full.

The vase in the shape of a cuboid has a height of 20·6 cm.
The radius of the base of the cylindrical vase is 6 cm.

The website states that both of these vases have the same height.
Is the website correct?
You must show all your working. [3]

The website is correct ☐ The website is incorrect ☐

Mark scheme

Scheme	Mark	Comments
Appropriate method, e.g. (Volume cylinder) \(\pi \times 6^2 \times 20.6\) (compared with 1648 cm\(^3\)) (Height cylinder) \(\pi \times 6^2 \times\) height = 1648 or (height =) \(\dfrac{1648}{\pi \times 6^2}\) (Area X-sections) \(\pi \times 6^2\) with 1648 / 20.6 (Radius cyl) \(\sqrt{\dfrac{1648 / 20.6}{\pi}}\) (compared with 6 cm)	M1
Correct evaluation for the method used, e.g. (Volume cylinder)(range) 2328(cm\(^3\)) to 2331(cm\(^3\)) (Heights) (range) 14.5(cm) to 15(cm) (Area X-sections) approximately 113 (cm\(^2\)) with (1648/20.6 =) 80 (cm\(^2\)) (Radius cylinder) approximately 5 (cm)	A1	Allow height 14(cm), provided not from incorrect working. Answer for height may be from a trial
‘Incorrect’ stated or indicated	A1	Depends on M1 A1 previously awarded If no marks, due to error in not using \(\pi r^2\) as the base area (in area or volume calculation), however ‘their \(\pi r^2\)’ does include a product including \(\pi\) and 6 (or embedded as 12), but otherwise method, accuracy and conclusion correct for ‘their \(\pi r^2\)’, award SC1