Higher June 2019 Paper 1 Q15
15 The diagram shows a solid shape.
The shape is a cone on top of a hemisphere.
The height of the cone is 10 cm.
The base of the cone has a diameter of 6 cm.
The hemisphere has a diameter of 6 cm.
The total volume of the shape is \(k\pi\) cm3, where \(k\) is an integer.
Work out the value of \(k\). (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 48 | M1 | for method to use a volume formula with correct substitution for the cone, sphere or hemisphere eg \(\dfrac{1}{3} \times \pi \times 3^2 \times 10\) or \(\dfrac{4}{3} \times \pi \times 3^3\) or \(\dfrac{2}{3} \times \pi \times 3^3\) oe |
| M1 | for complete method to find total volume eg \(\dfrac{1}{3} \times \pi \times 3^2 \times 10 + \dfrac{2}{3} \times \pi \times 3^3\) | |
| M1 | (dep first M1) for correct partial simplification, eg \(30\pi\) or \(18\pi\) | |
| A1 | cao | |
| SC B2 for answer of 264 or \(264\pi\) |
Additional guidance
May work without \(\pi\) or with an approximation of \(\pi\); must use the correct radius of 3 (and 10) in substitution
Must be cone or hemisphere
Accept \(48\pi\)