Question

It is given that A is directly proportional to r2 and r> 0. When r=5, A=75.

Find
(a)the value of A when r=4,
(b)the value of r when A=147

Answer 1

see explanation

Explanation:

Given A is directly proportional to r² then the equation relating them is

A = kr² ← k is the constant of proportion

To find k use the condition when r = 5, A = 75 , then

75 = k × 5² = 25k ( divide both sides by 25 )

3 = k

A = 3r² ← equation of proportion

(a)

when r = 4, then

A = 3 × 4² = 3 × 16 = 48

(b)

when A = 147 , then

147 = 3r² ( divide both sides by 3 )

49 = r² ( take the square root of both sides )

r =
`√(49)` = 7