Higher June 2017 Paper 1 Q15
15 A cone has a volume of 98 cm3.
The radius of the cone is 5.13 cm.
(a) Work out an estimate for the height of the cone. (3)
John uses a calculator to work out the height of the cone to 2 decimal places.
(b) Will your estimate be more than John’s answer or less than John’s answer?
Give reasons for your answer. (1)
Give reasons for your answer. (1)
| Answer | Mark | Notes |
|---|---|---|
| 3.5 to 4.5 | M1 | substitution into formula \(\dfrac{1}{3}\pi r^2 h\) of chosen values for \(r\) and \(V\) (accept \(r = 5.13\) and \(V = 98\)) and starts rearrangement e.g. multiplies by 3, divides by \(\pi\) or divides by \(r^2\) (both sides) |
| M1 | uses estimates in calculation e.g. \(\dfrac{3 \times 100}{3 \times 25}\) (or in rearranged formula) or \(\dfrac{12}{\pi}\) | |
| A1 | arrives at a single value from estimate in the range 3.5 to 4.5 |
| Answer | Mark | Notes |
|---|---|---|
| more | C1 | ft e.g. more since number in numerator goes up; numbers in denominator go down. |