Shape and Space 7
3 marks · NormalA closed cylindrical water tank has a diameter of 2 m and a height of 3.5 m.
Calculate:
The volume of the tank. Give your answer in cubic metres.
The total surface area of the tank (including top and bottom). Give your answer in square metres.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 11.0 m^3
(b) 34.6 m^2
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Uses correct volume formula: V = πr²h.
A1 (a) · 1 mark · Correctly finds volume as 11.0 m³ (3 s.f.).
M2 (b) · 1 mark · Uses correct surface area formula: 2πrh + 2πr², and evaluates to 34.6 m² (3 s.f.).
Worked solution
a) r = 1 m, h = 3.5 m; Volume = π × r² × h = π × 1² × 3.5 = 11.0 m³ (3 s.f.)
b) Surface area = 2πrh + 2πr² = 2π × 1 × 3.5 + 2π × 1² = 7π + 2π = 9π = 28.3 m² (curved) + 6.3 m² (top and bottom) = 34.6 m² (3 s.f.)