Chapter 12.1, Problem 41STP

(a)

To determine

To find the outer perimeter of the deck.

Answer to Problem 41STP

Outer Perimeter of deck $=128$ feet

Explanation of Solution

Given Information:

• A home maker wants to build a 3-foot-wide deck around his circular pool as shown below:

  

• Circumference of pool, C is 81.64 feet

Formula Used:

Circumference of circle $=\pi d$ , where d is the diameter

Calculation:

By using the formula of circumference of circle we can find the diameter of circle

Substituting the value of C in C $=\pi d$ we get

  $81.64=\pi \left(d\right)$

∴$d=\frac{81.64}{\pi }$

  $d=25.987\approx 26$ Feet

It can be shown in a diagram as:

  

Since the deck is 3 foot wide length of outer deck $=26+3+3$ = 32 feet

Therefore perimeter of outer deck = $4\left(\text{lenghth of a side}\right)$

  $=4\left(32\right)$

  $=128$

(b)

To determine

To find the area of the top of the deck.

Answer to Problem 41STP

Area of deck =348 sq. Feet

Explanation of Solution

Given Information:

Given Information:

• A home maker wants to build a 3-foot-wide deck around his circular pool as shown below:

  

• From part (a) Diameter of circle $=26$ feet

Formula Used:

Area of square $=a^2$

Calculation: $$

The deck consists of an outer square with a smaller inner square removed.

Area of deck = Area of outer square $-$ Area of inner square ………. (1)

  

From above diagram:

• For outer square

Length of side = 32 feet

Therefore, Area = ${32}^2=1024$ sq. Feet

• For inner square

Length of side = 26 feet

Therefore, Area = ${26}^2=676$ sq. Feet

  $\therefore (1)\Rightarrow$

Area of deck = $1024-676=348$ sq. Feet