Hint
Use the stated units and precision. Halve the sphere volume, retaining cubic units.
Worked solution
(a)
Halve the sphere volume, retaining cubic units.
Half the sphere volume gives coefficient \(\displaystyle \frac{2r^{3}}{3}=\)\(\displaystyle \frac{250}{3}\).
Answer: \(\displaystyle \frac{250}{3}\)
(b)
Add the two nonoverlapping component volumes.
Add cylinder coefficient 275 and hemisphere coefficient \(\displaystyle \frac{250}{3}\).
Answer: \(\displaystyle \frac{1075}{3}\)
(c)
Exclude the joined discs and include the one closed outer base.
The cylinder curve, hemisphere curve and one base give 2rh+2r²+\(\displaystyle r^{2}\)=185.
Answer: \(185\)
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: Halve the sphere volume, retaining cubic units.
- 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: Add the two nonoverlapping component volumes.
- 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: Exclude the joined discs and include the one closed outer 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.