EXERCISE 3.7

The surface area $A$ of a cube varies directly as the square of the length $l$ of an edge and $A = 27$ square units when $l = 3$ units.

Find (i) $A$ when $l = 4$ units (ii) $l$ when $A = 12$ sq. units.

The surface area $S$ of the sphere varies directly as the square of radius $r$ , and $S=16\pi$$S = 16\pi$ when $r = 2$ . Find $r$ when $S=36\pi$$S = 36\pi$ .

In Hook's law the force $F$ applied to stretch a spring varies directly as the amount of elongation $S$ and $F = 32lb$ when $S = 1.6$ in. Find (i) $S$ when $F = 50$ lb (ii) $F$ when $S = 0.8$ in.

The intensity $I$ of light from a given source varies inversely as the square of the distance $d$ from it. If the intensity is 20 candlepower at a distance of 12ft. from the source, find the intensity at a point 8ft. from the source.