O-LevelMathematicsMensuration4024/22 · May/June 2016 · Q1112 Marks
[Volume of a cone = ⅓ πr²h]
- (a)(i)Solid I is a cylinder with a small cylinder removed from its centre, as shown in the diagram. The height of each cylinder is 20cm and the radius of the small cylinder is rcm. The radius of the large cylinder is 3.5 cm greater than the radius of the small cylinder. The volume of Solid I is 3000 cm³. Calculate r. [Figure 11.1][4]
- (a)(ii)Solid II is a cone with volume of 3000cm³. The perpendicular height of the cone is twice its radius. Which solid is the taller and by how much? [Figure 11.2][4]
- (b)The diagram shows a triangular prism of length 24 cm. Its cross-section is an equilateral triangle with sides 8 cm. Calculate the total surface area of the prism. [Figure 11.3][4]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.
- [4] (a)(i) 5.06 to 5.08
- [4] (a)(i) B1 for r + 3.5 seen
- [4] (a)(i) B1 for π(r + 3.5)² – πr²
- [4] (a)(i) or 20π(r + 3.5)² – 20πr²
- [4] (a)(i) B1 for 20π(r + 3.5)² – 20πr² = 3000 or better
- [4] (a)(ii) Solid II by 2.5 – 2.6
- [4] (a)(ii) B3 11.25 to 11.3 cm
- [4] (a)(ii) or M1 for 1/3 × πr²×2r = 3000 or better
- [4] (a)(ii) and M1 for r³ = (3000×3)/(2×π) (= 1432)
- [4] (b) 630 to 632
- [4] (b) M1 for ½ × 8 × 8 × sin 60 or ½ × 8 × √48 oe
- [4] (b) M1 for 8 × 24 soi or 192 soi
- [4] (b) M1 for 3 × 8 × 24 + 2 × their (triangle area)
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →