If the volume of the expanding cube is increasing at the rate of 24 cm3/min, how fast is its surface area increasing when the surface area is 216 cm??
Answers
Answer:
The surface area is 216 cm is 16 cm^2/min
Step-by-step explanation:
Step 1: dV/dt=24
V=a^3, differentiate with respect to t
dV/dt=3a^2*da/dt, a^2*da/dt=8
S=6a^2, 216=6a^2. a=6. da/dt=(8/36)
dS/dt=12*a*da/dt=12*(8/6)=16 cm^2/min
Step 2: A cell's internal volume expands as it becomes bigger, which causes the cell membrane to do the same. Consequently, the volume grows faster than the surface area. As a result, less surface area is relatively accessible to transmit materials to a unit volume of the cell.
Step 3: A reactant's surface area affects both the number of collisions and the pace of reaction. One huge particle has a lesser surface area than several smaller ones. The reaction will happen more quickly the more surface area there is for particles to smash on.
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