O-LevelMathematicsMensuration4024/11 · Oct/Nov 2022 · Q237 Marks
23 [Volume of a cone = 1/3 πr²h, curved surface area of a cone = πrl] [Surface area of a sphere = 4πr²] A solid cone has radius y cm. The slant height of the cone is 25% larger than the radius of the cone. A solid sphere has radius R cm. The surface area of the sphere is equal to the total surface area of the cone. (a) Show that y = 4R/3 (b) Find the volume of the cone in terms of R. Give your answer as simply as possible.
- (a)Show that y = 4R/3[3]
- (b)Find the volume of the cone in terms of R. Give your answer as simply as possible.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [3] 4πR² = 5πy²/4 + πy² oe [M2]
- M1 for l = 5y/4 oe soi
- Completion to y = 4R/3 with no errors [A1]
- [4] 16πR³/27 final answer
- B2 for vertical height = 3y/4 or R
- or M1 for h² + y² = (5y/4)² oe or h² + (4R/3)² = (5/4 * 4R/3)² oe
- M1 for 1/3 πy²h or 1/3 π(4R/3)²(R) with their vertical height
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 →