4MA0 Higher June 2017 Paper 3R Q19
19 The diagram shows two solid shapes, shape A and shape B.
Shape A is made of a hemisphere and a cone.
Shape B is a cylinder.
Diagram NOT accurately drawn
For shape A
radius of the hemisphere is 36 cm
radius of the base of the cone is 36 cm
height of the cone is 53 cm
For shape B
radius of the cylinder is \(r\) cm
height of the cylinder is \(2r\) cm
The volume of shape A = the volume of shape B
Calculate the height of shape B.
(6)
| Scheme | Marks |
|---|---|
| (\(V_c =\)) \(\dfrac{\pi}{3} \times 36^2 \times 53\) (\(=22896\pi = 71930\)) | M1 |
| (\(V_H =\)) \(\dfrac{2\pi}{3} \times 36^3\) (\(=31104\pi = 97716\)) | M1 |
| \(\pi \times r^2 \times 2r = \text{“}\dfrac{2\pi}{3} \times 36^3\text{”} + \text{“}\dfrac{\pi}{3} \times 36^2 \times 53\text{”}\) oe | M1 |
| \(r = \sqrt[3]{\dfrac{\text{“}54000\pi\text{”}}{2\pi}} = 30\) | M1 |
| 2 × “30” | M1 |
| 60 | A1 |
| (6) | |
| (6 marks) |
Notes
M1: for volume of cone
M1: for volume of hemi-sphere
NB : \(54000\pi\) or 169646 implies first two method marks
M1: (dep on at least M1)
for forming an equation with correct volume expression for cylinder
M1: (dep previous M1)