Question

If each side of a cube is increased by 1%, the percentage change in volume would be approximately

Answer 1

If each side of a cube is increased by 1%, the percentage change in volume would be approximately

solution : volume of cube = (side length)³

if we assume V is the volume of cube, and l is side length of cube then, V = l³

a/c to question, each side of a cube is increased by 1% . it seems very small change in side so, we have to use formula, ∆V/V = 3 × ∆l/l

or, % change in V = 3 × % change in l

= 3 × 1 % = 3%

hence, percentage change in volume would be approximately 3%

Answer 2

Answer:

3.03 % increase in Volume

Step-by-step explanation:

Let say side of cube = a

Volume of cube = a³

Side of cube increased by 1%

increased size = a + (1/100)a = 1.01a

Increased Volume = (1.01a)³ = 1.030301a³

increase in Volume = 1.030301a³ - a³

= 0.030301a³

% increase in volume = (0.030301a³/a³ ) * 100

= 3.0301  %

≈ 3.03 % increase in Volume