Higher June 2025 Paper 1R Q26
26 R, S and T are three similar vases.
Diagram NOT accurately drawn
The volume of vase S is 72.8% more than the volume of vase R
The height of vase R is \(h\) cm
The height of vase T is \(6h\) cm
The surface area of vase S is \(A\) cm2
The surface area of vase T is \(kA\) cm2
Work out the value of \(k\)
(4)
| Scheme | Marks |
|---|---|
eg \(\sqrt[3]{1.728}(= 1.2)\) oe or (length R : S =) 1 : 1.2 oe eg 5 : 6 or (length R : S : T =) 1 : 1.2 : 6 oe eg 5 : 6 : 30 or (volume S : T = ) 1.728 : 216 or 216 ÷ 1.728 (= 125) | M1 |
eg 6 ÷ “1.2” (= 5) or \(\sqrt[3]{\dfrac{216}{1.728}}(= 5)\) (length S : T =) 1 : 5 or \(\sqrt[3]{1.728} : \sqrt[3]{216}\) (area S : T =) “1.2”2 : 62 oe or (area S : T =) 62 : 302 oe or (area R : S : T =) 1 : “1.2”2 : 62 oe or (area R : S : T =) 52 : 62 : 302 oe | M1 |
eg “5”2 or (area S : T =) 12 : “5”2 or (area S : T =) 1 : 25 or \((k =)\dfrac{36}{1.44}\) oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 25 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for method to find the scale factor between the heights of R and S or
for a correct ratio for the lengths R : S or
for a correct ratio for the lengths R : S : T
or for a correct ratio or scale factor for the volumes S : T
M1: for method to find the scale factor between the heights of S and T or
for a correct ratio of the heights of S and T in the form 1 : \(n\) or
for a correct method to find the ratio for the areas S : T ft their ratio of lengths
or for a correct method to find the ratio for the areas R : S : T ft their ratio of lengths (maybe seen as the two separate ratios of R : S and R : T)
M1: for squaring the scale factor of the heights of S and T or
for a correct ratio in the form 1 : \(n\) for the areas S : T ft their ratio of areas, may be implied by their final answer or
for a correct calculation using the area ratio of S : T to find the value of \(k\)
A1: cao