Question

We need to store 1l of cold water in warm weather for as long as possible. In which of the following shapes should a flask be built for the task. Assume the thickness and material are same for all the shapes.

• A. Cubical
• B. Conical, with radius=height
• C. Spherical
• D. Cylindrical, with radius=height

Answer 1

The correct option is C

Spherical

For all modes of heat transfer $\Delta Q\propto Area$,A.So we should choose the shape with minimum area for minimum heat transfer.

(a)For cubical:

Volume, V = $a^3=1l$,$\therefore a=1dm\left(decameter\right)$

Area, A = $6a^2=6d{m}^2$

(b)For conical: V= $\frac{\pi r^{2}h}{3}$, but given r=h,$r=\frac{3\frac{1}{3}}{\pi }$ dm

A=$\pi r\left(\sqrt{2r}\right)+\pi r^2$

= 7.354 $d{m}^2$

(c)For Sphere:

$V=\frac{4}{3}\pi r^3$, $\therefore r=(\frac{3}{4}{)}^{\frac{1}{3}}dm$

A$=4\pi r^2=4.84d{m}^2$

(d) For Cylinder:

$V=\pi \times r^2\times r\therefore r=\frac{1}{\pi \frac{1}{3}}dm$

A=$2\pi r^2+2\pi r.r=5.86d{m}^2$

As Sphere has the least area among these, it will be the shape with minimum heat loss. In fact sphere is the shape with the minimum surface area among all possible shapes!