Question

The volume of a sphere is V(r) = 43

πr3 and the radius is increasing 2 mm per second. The function r(t) = 2t gives the radius at time t seconds. Which function gives the volume at time t?

A. (V ∘ r) (t)
B. (r ∘ V) (t)
C. (r + V)(t)
D. (V • r)(t)

Answer 1

It’s A I hope this helps

Answer 2

Answer: Option A.

Explanation:

The function for the volume of a sphere is given by V(r) = (4/3)πr^3.

The radius of the sphere is increasing at a rate of 2 mm per second, which means that the radius at time t seconds is given by r(t) = 2t mm.

To find the volume of the sphere at time t, we can substitute the expression for r(t) into the formula for the volume of the sphere:

V(t) = (4/3)πr(t)^3

= (4/3)π(2t)^3

= (4/3)π(8t^3)

= (32/3)πt^3

V(t)= (32/3)πt^3

(V ∘ r)(t) = V(r(t))

= V(2t)

= (32/3)πt^3

Therefore, the function that gives the volume of the sphere at time t is option A.