Algebra 6

4 marks · Hard

The cost of producing a metal container varies as the square of its base diameter and is inversely proportional to its height . When cm and cm the cost is £64.

(a)

Write down a formula for in terms of and .

[1 mark]

(b)

Calculate the cost when cm and cm, giving your answer to 2 decimal places.

[3 marks]

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) C = k \frac{d^2}{h}

(b) £80.00 £

Common mistakes: using the wrong powers; incorrectly rearranging proportionality

Show mark scheme and worked solution

Marking points

B1 (a) · 1 mark · States or writes correct proportionality formula:

M1 (b) · 1 mark · Substitutes all known values to find

M2 (b) · 1 mark · Correctly substitutes new values into the derived formula (follow-through)

A1 (b) · 1 mark · Gives correct final answer to 2 decimal places (£80.00) (follow-through)

Worked solution

a) Since C varies as the square of d and inversely as h,

b) Substitute the values given to find k:

So,

Now use d = 25, h = 10:

But checking all working: 0.8 x (625 ÷ 10) = 0.8 x 62.5 = 50.

So the answer should have been £50.00 (amended from the earlier value, reflecting the correct working, as the formula evaluates directly to £50).