4MA0 Higher January 2014 Paper 4 Q23
23 A pyramid has a horizontal square base \(ABCD\) with sides of length 230 metres.
\(M\) is the midpoint of \(AC\).
The vertex, \(T\), is vertically above \(M\).
The slant edges of the pyramid are of length 218 metres.
Calculate the height, \(MT\), of the pyramid.
Give your answer correct to 3 significant figures.
Diagram NOT accurately drawn
(5)
| Scheme | Marks |
|---|---|
| \((AC^2 =)\; 230^2 + 230^2\) (= 105800) | M1 |
| \((MC =)\) ½ √(“105800”) (=162.6..) | M1 |
| \((MT^2 =)\; 218^2 - \text{“}162.6\text{”}^2\) (=21074) | M1 |
| (MT=) √“21074” | M1 |
| 145 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: M1 for \((MC^2) = 115^2 + 115^2\) (=26450)
M1: M1 for √(“26450”) (=162.6..)
M1: or M1 for correct trig working leading to one correct acute angle in MCT {either 41.8 or 48.2}
M1: or M1 for correct trigonometry working leading to correct answer
A1: Accept awrt 145