Unit 2
4 marks · NormalThe diameter of a circular pond is 14 m. Water is being added at a rate that increases the depth from 0.9 m to 1.15 m over 5 hours.
Write the formula for calculating the volume of water added, using π, diameter and change in depth.
Calculate the volume of water added to the pond over 5 hours. Give your answer to the nearest whole number.
Express your answer to part (b) in standard form.
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) V = π × (d/2)² × h
(b) 66 m³
(c) 6.6 × 10¹ m³
Common mistakes: Incorrect formula; Incorrect use of diameter for radius
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · Correct formula for volume of a cylinder.
M1 (b) · 1 mark · Calculates change in depth and applies formula.
A1 (b) · 1 mark · Correctly calculates answer as 66 m³ (to nearest whole number).
A2 (c) · 1 mark · Gives answer as 6.6 × 10¹ m³ in standard form.
Worked solution
a) Volume V = π × (d/2)² × h, where d = diameter, h = change in depth.
b) h = 1.15 - 0.9 = 0.25 m, d = 14 m, r = 7 m. V = π × 7² × 0.25 ≈ 38.5 × 0.25 ≈ 66 m³.
c) 66 m³ in standard form is 6.6 × 10¹ m³.