Chapter 12.7, Problem 17IP

a)

To determine

To find : Amount6 of ice in icicle.

Answer to Problem 17IP

  $1.47{\text{ ft}}^{\text{3}}$

Explanation of Solution

Given Information :

We know that diameter = $1.5$ ft. and height = $2.5$ ft.

Formula Used:

Volume of cone = $\frac{1}{3}\pi r^{2}h$

Calculation :

The amount of ice in icicle = $\frac{1}{3}\pi r^{2}h$

  $\begin{array}{l}=\frac{1}{3}(3.14){\left(\frac{1.5}{2}\right)}^2(2.5)\\ =1.47{\text{ ft}}^{\text{3}}\end{array}$

As Radius = $\frac{\text{diameter}}{\text{2}}=0.75$ feet.

b)

To determine

To find : How much time to melt icicle.

Answer to Problem 17IP

  $75$ minutes

Explanation of Solution

Given Information :

Icicle melts at a rate of $0.1{\text{ ft}}^{\text{3}}$ in every $5$ minutes.

Calculation :

The icicle melts at a rate of $1{\text{ft}}^{\text{3}}=\frac{5}{0.1}=50\text{ min}\text{.}$

So,

Icicle melts at a rate of $1.5{\text{ft}}^{\text{3}}$ in every min.

  $=50\times 1.5$

  $=75$ minutes.

Hence, it takes $75$ minutes to icicle melt.