Answer:
The effect of doubling the diameter is increased the area to paint as 4 times. So, paint needed is 4 times than it was before. And the area is increased by 9 times when the diameter is increased by a factor of 3. So, paint needed is 9 times than before.
Step-by-step explanation:
Please remember the concept
If side lengths are in the ratio a : b
Then the area are in the ratio of a^2 :b^2
The volume are in the ratio of a^3 :b^3,
When diameter is doubled, the area ratio becomes
which is simplified to ![x^{2} :4x^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%3A4x%5E%7B2%7D)
So, the area is increased by 4 times.
According to this concept , the diameter is increased by the scale factor 3.
Let the diameter of tank is 'x', so the diameter becomes "3x"
So, it's area ratio would be ![x^{2} :(3x)^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%3A%283x%29%5E%7B2%7D)
If we simplify it we get ![x^{2} :9x^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%3A9x%5E%7B2%7D)
We conclude that area to be increased by 9 times.