Question

questions 4 and 5 refer to the following. a liquid storage tank is in the shape of a right circular cylinder with a radius of 10 feet, as shown. the tank initially contains some water. at time ( t = 0 ), more water starts flowing into the tank. the height of the water in the tank ( t ) seconds after the water starts flowing into the tank is modeled by the function ( h(t)=0.2 t ), where ( 0 leq t leq 210 ). 4 mark for review the function ( v ) represents the volume of the water in the tank in terms of the height of the water. which of the following functions expresses the volume of water in the tank in terms of the number of seconds ( t ) after the water starts flowing into the tank? a ( v(h(t)) ) b ( h(v(t)) ) c ( v(t) cdot h(t) ) d ( v(t)+h(t) )

Explanation:

Step1: Understand function composition

We need to find the volume of water in the tank in terms of the number of seconds \(t\) after water starts flowing. The volume \(V\) is a function of height \(h\) (since \(V=\pi r^{2}h\) for a cylinder, here \(r = 10\) is constant, so \(V=100\pi h\)), and height \(h\) is a function of time \(t\) (\(h(t)=0.2t\)).

Step2: Substitute the function of \(h\) into \(V\)

To get the volume as a function of time, we substitute \(h(t)\) into \(V(h)\). That is, we use the composition \(V(h(t))\).

Answer:

A. \(V(h(t))\)