Given that P varies directly as the square of r, and P = 48 when r = 4, calculate the valu… — JAMB UTME

Given that $P$ varies directly as the square of $r$ , and $P = 48$ when $r = 4$ , calculate the value of $P$ when $r = 6$ .

Answer: 108

The value of

P

when

r = 6

108

Since

P

varies directly as

r^2

, the relationship is expressed as

P = k r^2

. Substituting the given values

P = 48

and

r = 4

yields

48 = 16k

, so

k = 3

. Substituting

k = 3

and

r = 6

into the equation gives

P = 3 \times 6^2 = 3 \times 36 = 108

Set up the variation equation using constant of variation

k

P = k r^2

Direct variation with the square of a variable means

P

is directly proportional to

r^2

Substitute the initial values

P = 48

and

r = 4

to determine

k

48 = k \times 4^2 \implies 48 = 16k \implies k = 3

Finding the variation constant

k

allows us to establish a specific relationship between

P

and

r

Calculate

P

for

r = 6

using the specific equation

P = 3 r^2

P = 3 \times 6^2 = 3 \times 36 = 108

Evaluating the formula with the new input

r = 6

yields the required value of

P

Direct variation involving square powers

Question