An inverted right circular conical tank has an altitude to 7 feet and a base with radius 1.25 feet. Find the dimensions and the volume of a similar tank whose volume is three times as much as the first conical tank.

Question

anonymous · Answer

There can be many such tanks. I'll keep the height fixed, for simplicity.
$$V=\frac{1}{3}\pi r^2 h = \frac{1.25^2*7\pi}{3}$$ Let's call the volume of our new tank W. W=3V.
$$W=3V=1.25^2*7\pi$$Since I decided to keep the height fixed. We only need the radius of our new tank.
$$W = 1.25^2*7\pi = \frac{1}{3}\pi R^2 H$$Since H=7, we cancel out H and pi.
$$1.25^2=\frac{R^2}{3}$$$$R=\sqrt{3*1.25^2}\approx2.165$$

anonymous · Answer

I have the same answer... but will it also work if the one you retain is the radius?

anonymous · Answer

Yes. Let's try that.
$$W=1.25^2*7\pi=\frac{ 1 }{ 3 }\pi R^2 H$$$$7=H/3$$$$H=21$$
In fact, the new H = h*3. This is because the volume is linearly dependent on height.

anonymous · Answer

ahh...I see thank you very much!!! ^^

anonymous · Answer

Anytime! ^^