Question

The side, a, of a cube, has been measured as a = (2.5 ± 0.1) cm The total surface area (S), and the volume (V), of the cube, would be expressed as

(1) S = (38 ± 3) cm² V = (15.625 ± 1.875) cm³

(2) S = (37.5 ± 3) cm² V = (15.63 ± 1.88) cm³

(3) S = (37.5 ± 3) cm² V = (15.6 ± 1.9) cm³

(4) S = (38 ± 3) cm² V = (16 ± 2) cm³

Answer 1

(4) S = (38 ± 3) cm2 V = (16 ± 2) cm³

We have,

Total surface area, S = 6 (a²)

= 6 (2.5)² cm² = 37.5 cm²

Also,

\(\frac{ΔS}{S}=2\frac{Δa}{a}=\frac{2\times 0.1}{2.5}=0.08\)

∴ ΔS = (0.08 x 37.5)cm² = 3 cm²

We should, therefore, express S as,

S = (38±3)cm²

Also volume V = a³ = (2.5)³ cm³ = 15.625 cm³

∴ \(\frac{ΔV}{v}=3\frac{Δa}{a}=\frac{3(0.1)}{2.5}=0.12\)

∴ ΔV = 0.12 x 15.625cm³ = 1.875cm³ ≈ 2 cm³

We, should, therefore, express V as

V = (16±2) cm³