Higher June 2019 Paper 1 Q17
17 A and B are two similar vases.
Diagram NOT accurately drawn
Vase A has height 24 cm.
Vase B has height 36 cm.
Vase A has a surface area of 960 cm2
(a) Work out the surface area of vase B. (2)
Vase B has a volume of \(V\) cm3
(b) Find in terms of \(V\), an expression for the volume, in cm3, of vase A. (2)
| Scheme | Marks |
|---|---|
| eg \(\dfrac{24}{36}\) or 2 : 3 oe or \(\dfrac{36}{24}\) or 3 : 2 oe | M1 |
| 2160 | A1 |
| (2) |
Notes
M1: for a correct scale factor
| Scheme | Marks |
|---|---|
\(\left(\dfrac{24}{36}\right)^3\) or \(2^3 : 3^3\) oe or \(\left(\dfrac{36}{24}\right)^3\) or \(3^3 : 2^3\) oe or \(\dfrac{8}{27}\) or \(\dfrac{27}{8}\) oe | M1 |
| (A =) \(\dfrac{8}{27}V\) oe | A1 |
| (2) | |
| (4 marks) |
Notes
M1: For correct SF for volume
ft from linear scale factor in (a)
or ft from \(\sqrt{\dfrac{\text{``}{2160}\text{''}}{960}}\)
A1: oe eg \(\dfrac{V}{3.375}\)