SPM 2023 Add Maths Paper 2, Question 3Differentiation

Solved on video in English and Bahasa Melayu · Form 5, Differentiation · 5:28 video

The question

(a)

A closed cylindrical tank has a height of h metres and a radius of r metres. The tank can be fully filled with (125/4)π m³ of water. [Use π = 3.142]

(a) Find the total surface area, in m², of the tank in terms of π and r.

(b)

A closed cylindrical tank has height h metres and radius r metres, and can be filled with (125/4)π m³ of water. [Use π = 3.142]

(b) The tank is made of a material that costs RM720 per m². Calculate the minimum cost of the material required to make the tank.

Step 1

Volume of cylinder: πr² h = (125/4)π → r² h = 125/4 → h = 125/(4r².

Why this step

The volume is fixed, so it links h and r. Solving for h lets us write the area using r only, ready to minimise in (b).

3 more steps, each with the reason for it, in the full solution

Final answer

A = 2πr² + 125π/(2r)

Where students lose marks

Watch out: simplify carefully. 2πr × 125/(4r² = 125π/(2r), not 125π/r. Keep the 2 in the denominator.

6 more steps, each with the reason for it, in the full solution

Final answer

Minimum cost = RM84 834

Where students lose marks

Watch out: a wrong area in (a) carries through to r and the cost. Check 125π/(2 × 5/2) = 25π when substituting back.

Watch every step of this question solved on video (5:28), with the reason behind each step and a box that checks your own answer.

No card. Every past-year question on video, in English and BM.