Answer:
Snow ball is melting with a rate of 0.265 cm per minute.
Step-by-step explanation:
Snow ball is a sphere in shape, so surface area of the ball will be represented by the formula,
S = 4πr²
If snow ball is melting, then [tex]\frac{dS}{dt}=3[/tex] cm² per minute
We have to find the rate of decrease in the diameter of the snow ball when the radius of the ball is = [tex]\frac{9}{2}=4.5[/tex] cm
Now [tex]\frac{dS}{dt}=4\pi \frac{d}{dt}(r^{2})[/tex]
[tex]3=4\pi (2r)\frac{dr}{dt}[/tex]
[tex]3=4\pi (9)\frac{dr}{dt}[/tex]
[tex]\frac{dr}{dt}=\frac{3}{36\pi}[/tex]
[tex]\frac{dr}{dt}=0.0265[/tex] cm per minute
Therefore, the snow ball is melting with a rate of 0.265 cm per minute.
