Question

10. A solid rectangular block has a base which measures 3x cm by 2x cm, the height is y cm, and its volume is 72 cm³.
(a) Express y in terms of x;
(b) Find: (i) an expression for the total surface area of the block in terms of x only; (ii) the value of x for which the total surface area has a stationary value.

Accepted Answer

(a) Volume = 3x×2x×y = 6x²y = 72, so y = 12/x².
(b)(i) Total surface area S = 2(3x×2x + 3xy + 2xy) = 12x²+10xy. Substituting y=12/x²: S = 12x² + 120/x.
(ii) dS/dx = 24x − 120/x² = 0 → 24x³=120 → x³=5 → x = ³√5 ≈ 1.71 cm (this gives the stationary/minimum surface area).

WAEC Further Mathematics 2022 Theory — Question 10

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