The polynomial function defined by

f left parenthesis x right parenthesis equals StartFraction pi Over $3$ EndFraction x cubed minus $5$ pi x squared plus StartFraction $500$ pi d Over $3$ EndFractionf$($x$)=$$3$x$35$x$2+500$d$3$

can be used to find the depth that a ball

$1010$

cm in diameter sinks in water. The constant d is the density of the$$ball$,$ where the density of water is $1.$ The smallest positive zero of$$f$($x$)$ equals the depth that the ball sinks$.$ Approximate this depth for each material and interpret the results.

$$a$)$ A wooden ball with

d equals $0\mathrm{.}7.$d$=0\mathrm{.}7.$

$$b$)$ A solid aluminum ball with d equals $2\mathrm{.}4.$d$=2\mathrm{.}4.$

$$c$)$ A spherical water balloon with d equals $1.$d$=1.$

$...$

Question content area right

Part $1$

$$a$)$ Select the correct choice below and fill in any answer boxes in your choice.

A$.$

The depth is

enter your response here

$$

$($Type an integer or decimal rounded to the nearest hundredth as$$needed$.)$

B$.$

The answer is undefined.