Question

If A=kr² and V=kr³, find the percentage increase in A and V if r is increased by 20%​

Answer 1

Answer:

The percentage increase in A is 44%. The percentage increase in V is 72.8%.

Step-by-step explanation:

The easiest way to go about solving this problem is to pick your own numbers and plug them into the given equations.

For example, let's say that k = 5 and that r = 10.

$A=kr^{2}$  ⇒ $A= 5 * 10^{2} =500$

$V=kr^{3}$ ⇒ $V= 5 * 10^{3}= 5000$

The question is asking, what is the percentage increase if r is increased by 20%. Our chosen k-value will stay the same but our r-value is going to increase. To find the new value of r, we multiply 10, our current value of r, by 1.2. This gives us a new value for r, which is 12.

$10*1.2=12$

Now, we are going to plug in our new r-value and our k-value into the given equations. k = 5; new r = 12

$A=kr^{2}$ ⇒ $A=5*12^{2}=720$

$V=kr^{3}$ ⇒ $V=5*12^{3}=8640$

Next, we have to calculate the percentage increase in our values of A and V. To do this, we use the following formula:

$Percentage Increase = \frac{final - initial}{initial} * 100$

Percentage Increase for A

Initial value: 500

Final Value: 720

$Percentage Increase = \frac{720-500}{500} * 100 = 44%$

Percentage Increase for V

Initial value: 5000

Final Value: 8640

$Percentage Increase= \frac{8640-5000}{5000} *100 = 72.8%$

The percentage increase for A is 44% and the percentage increase for V is 72.8%.

Hope this helps!