Chapter 8.6, Problem 51PPS

(a)

To determine

To Find: Surface area of water.

Answer to Problem 51PPS

The surface area of water is 500 sq feet.

Explanation of Solution

Given information:

Model A:

Volume:1750 cubic feet

Depth: 42 inches

Length=Width + 5feet

Expression for volume is

  $V=x\times (x+5)\times 3.5$

  $1750=x\times (x+5)\times 3.5$

  $x\times (x+5)=\frac{1750}{3.5}$

  $A=500$ sq feet.

(b)

To determine

To Find: Dimensions of the pool.

Answer to Problem 51PPS

Width $=20$ feet

Length $=25$ feet

  $x^2+5x-500=0$

Explanation of Solution

From above,

  $x\times (x+5)=500$

  $x^2+25x-20x-500=0$

  $(x+25)(x-20)=0$

  $x=20$ Ignore negative value

Length $=20+5=25$$\text{Width}=20$

(c)

To determine

To find: Possible dimensions for the given pool.

Answer to Problem 51PPS

Possible dimension:

  $20\text{ft}\times 25\text{ft}\times 7\text{ft}$ ,

  $20\text{ft}\times 50\text{ft}\times 3.5\text{ft}$ ,

  $40\text{ft}\times 25\text{ft}\times 3.5\text{ft}$

Explanation of Solution

Volume of model A written as :

  $V=20\ast 25\ast 3.5$

Volume of model B written as :

  $V=20\ast 25\ast 3.5\ast 2=1750\ast 2$

Possible dimension:

  $20\text{ft}\times 25\text{ft}\times 7\text{ft}$ ,

  $20\text{ft}\times 50\text{ft}\times 3.5\text{ft}$ ,

  $40\text{ft}\times 25\text{ft}\times 3.5\text{ft}$

(d)

To determine

To Explain: Ratio of volume of Model A to Model C

Answer to Problem 51PPS

Ratio of model A to model C : $V=\frac{1750}{7000}=0.25$

Explanation of Solution

Volume of model A written as :

  $V=20\ast 25\ast 3.5$

Volume of model C written as :

  $V=(20\times 2)(25\times 2)3.5=7000\text{cubicfeet}$

Since Width and length is twice for model C as model A

Ratio of model A to model C : $V=\frac{1750}{7000}=0.25$