⚡ Show ALL working — the AI awards method marks just like a real examiner. Partial credit for correct working even if the final answer is wrong.
1 markSector area4MA1 style
A sector has radius 8 cm and angle 135°. What is its area?
A 75.4 cm²
B 150.8 cm²
C 50.3 cm²
D 301.6 cm²
3 marksVolume of cylinder and cone4MA1 style 🔢 Calculator
A cone has radius 5 cm and height 12 cm. (a) Calculate the volume. (b) Calculate the slant height and curved surface area. Leave answers in terms of π where appropriate. (3 marks)
Hint: (a) V = ⅓πr²h. (b) Slant height uses Pythagoras: l = √(r²+h²). Then curved SA = πrl.
A swimming pool is a prism with trapezoidal cross-section. The trapezium has parallel sides 1.2 m and 2.5 m, and width 25 m. The pool is 50 m long. Calculate the volume of water needed to fill it. (4 marks)
Hint: Volume of prism = cross-sectional area × length. Cross-section is a trapezium: A = ½(a+b)h.
+40 XP
3 marksSphere and cylinder combined4MA1 style 🔢 Calculator
A hemisphere of radius 4 cm is attached to a cylinder of the same radius and height 10 cm. Calculate the total volume and total surface area. (3 marks)
Hint: Volume: hemisphere = ½ × (4/3)πr³. Cylinder = πr²h. Surface area: flat base of cylinder + curved cylinder + curved hemisphere (no flat circle at top — it joins the hemisphere).
+30 XP
1 markVolume conversion4MA1 style
A container holds 2.5 litres. What is this in cm³?