What is the rate of increase of its area at the moment when the side is 16cm long?

Question

A square plate of metal is expanding under the action of heat, and its side is increasing at the uniform rate of 0.1 cm per hour. What is the rate of increase of its area at the moment when the side is 16cm long?

Answer 1

HINT

Let

• $A(t)=(L_0+0.1\cdot t)^2$
• $A'(t)=2\cdot (L_0+0.1\cdot t)\cdot 0.1$

with

• $(L_0+0.1\cdot t)=16$

Answer 2

$A=a^2$

$\dfrac{dA}{dt}=2a\dfrac{da}{dt}$

put $a=16$ and and $\dfrac{da}{dt}=0.1$

$\dfrac{dA}{dt}=3.2 cm^2/sec$