The length of a pencil lcm, varies directly with it's mass, mg, and inversely with it's area of cross-section, Acm². When m=4 and A=0•4, I=18.
A. Find the formula connecting l, m and A
B. Hence find the length of a pencil which has a mass of 3g and a cross-sectional area of 0•5²
L = km/A
That means that AL/m is constant. You want L such that
0.5*L/3 = 0.4*18/4
Certainly, apologies for the confusion earlier. Here's the solution:
Given that the length of a pencil, L, varies directly with its mass, m, and inversely with its area of cross-section, A, we have:
L ∝ m/A
L = k(m/A) (where k is the constant of proportionality)
When m = 4 and A = 0.4, we have L = 18. To find the value of k, we substitute the given values:
18 = k(4/0.4)
18 = k(10)
k = 1.8
Therefore, the formula connecting L, m, and A is given by:
L = 1.8(m/A)
To find the length of a pencil that has a mass of 3g and a cross-sectional area of 0.5² cm², we substitute these values into the formula:
L = 1.8(3/0.5²)
L = 1.8(3/0.25)
L = 1.8(12)
L = 21.6 cm
Therefore, the length of the pencil is 21.6 cm.
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