The Pentagon Is Planning to Build a New Satellite That $V = \frac { 4 } { 3 } \pi r ^ { 3 }$

Multiple Choice

The Pentagon is planning to build a new satellite that will be spherical. As is typical in these cases, the specifications keep changing, so that the size of the satellite keeps growing. In fact, the radius of the planned satellite is growing 0.9 foot/week. Its cost will be $1,400 per cubic foot. At the point when the plans call for a satellite 8 feet in radius, how fast is the cost growing (The volume of a solid sphere of radius r is $V = \frac { 4 } { 3 } \pi r ^ { 3 }$ .)

A) $\frac { \mathrm { d } P } { \mathrm {~d} t } = \frac { \$ 3,584,000 \pi } { \text { week } }$
B) $\frac { \mathrm { d } P } { \mathrm {~d} t } = \frac { \$ 40,320 \pi } { \text { week } }$
C) $\frac { \mathrm { d } P } { \mathrm {~d} t } = \frac { \$ 230 \pi } { \text { week } }$
D) $\frac { \mathrm { d } P } { \mathrm {~d} t } = \frac { \$ 161,280 \pi } { \text { week } }$
E) $\frac { \mathrm { d } P } { \mathrm {~d} t } = \frac { \$ 322,560 \pi } { \text { week } }$