Question

Suppose V(r) = (4/3)*PiR^3 and p(t) = V(3t). Evaluate and simplify p(4).

Answer 1

2304 pi is one answer.

7238.2 is another. Depends on what you have been given

Explanation:

Givens

V(r) = (4/3) pi r^3

P(t) = V(3t)

Step One

Find the general equation for P(t)

V(3t) = (4/3) pi r^3 put 3t in for r

V(3t) = (4/3) pi (3t)^3 Show substitution

V(3t) = (4/3) pi 27 t^3 Cube the brackets

p(t) = (4/3) pi 27 t^3

Step Two

Find p(4)

p(4) = (4/3) pi 27 (4)^3 Substitute

p(4) = 4/3 PI 27 * 64 Cube the result

P(4) = 256 Pi * 27 / 3 Divide by 3

P(4) = 256 Pi * 9

p(4) = 2304 * pi Combine factors on the right.

What you do next depends on what answers you have been given. The answer above is one possible answer.

p(4) = 2304 * 3.14 is another

p(4) = 7238.2