Hint
Use the stated units and precision. Use the right triangle between radius, perpendicular height and slant height.
Worked solution
(a)
Use the right triangle between radius, perpendicular height and slant height.
Pythagoras gives \(\displaystyle \sqrt{r^{2}+h^{2}}=15 \mathrm{cm}\).
Answer: \(15\)
(b)
Use perpendicular height in the cone volume formula.
The coefficient \(\displaystyle \frac{r^{2}h}{3}\) is \(324\).
Answer: \(324\)
(c)
Include both the slant-height curved surface and circular base.
Curved area plus base gives coefficient rl+\(\displaystyle r^{2}\)=216.
Answer: \(216\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Use the right triangle between radius, perpendicular height and slant height.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Use perpendicular height in the cone volume formula.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Include both the slant-height curved surface and circular base.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 6 marks.