Question

Amit Kumar has an above ground pool in the shape of a regular octagon.

Opposite sides are 25 feet apart and each side is 10.4 feet long. It requires 7.5 gallons to fill one cubic foot.

How much water is need to fill the pool with 3 feet of water. A. 3900 B. 5850 C. 1560 D. 11700​

Answer 1

$\bf \huge{Answer}$

$\bf\green{D \: is \: correct \: option}$

$\bf\huge{EXPLANATION}$

Step-by-step explanation:

• To solve this question we can use the area formula for an octagon.

• It is as follows:

$\bf{A=2(1+√2)a²}$

• where "A" is the total area and "a" is the length of a side.

Plug in our side length a=10.4

$\bf{A=2(1+√2)10.4^2} \\\\ {≈522.24268}$

• Alternatively, you can split the octagon into 8 equal triangles.

The base of each triangle would be 10.4 and the height would be 12.5 since opposite sides are 25 feet apart. (25/2)

• The area of a triangle would then be:

$\bf{A=1/2bh}$

• where "b" is base and "h" is height

$\bf \pink{A=125 \times 10.4 \times 1/2=65}$

• Since there are 8 we multiply that by 8 for the area of an octagon

$\bf \red{65 \times 8=520}$

• The area of the octagon base is 520 square feet.

I'll use this value to do my calculations as it is more exact.

• Now, using this area, we need to find the volume of the pool we are meant to fill.

To do this, we simply multiply the area of the base by the height.

$\bf{520 \times 3=1560}$

• Now, we know that the volume of the pool is 1560 cubic feet.

Each cubic foot takes 7.5 gallons to fill.

$\bf{1560 \times 7.5=11700}$

• Therefore, the pool takes 11700 gallons of water to fill.

Answer 2

SOLUTION :-

To find the area of octagon,

We know that,

$\sf \fbox{A = 2(1 + \sqrt{2}) {a}^{2} }$

Here,

A = Total Area

a = Length

Given Length = 10.4 feet

$\sf {A = 2(1 + \sqrt{2}) {10.4}^{2} }$

$\sf {A = 2(1 + 1.4142135624) \times 108.16}$

$\sf {A = 2(2.414213564) \times 108.16}$

$\sf {A = 4.8284271248 \times 108.16}$

$\sf {A = 522.2426778184}$

$\sf \red{A ≈ 522.242678}$

An octagon can be split into 8 equal triangles.

Measures of triangle would be :-

• Bases = 10.4
• Height = 12.5 (Opposite sides are 25 so it will be $\sf{ \frac{25}{2}}$)

We know that,

$\sf \fbox{Area \: of \: triangle = \frac{1}{2} \times b \times h}$

Here,

b = base (10.4)

h = height (12.5)

So,

$\sf{→ \frac{1}{2} \times 10.4 \times 12.5}$

$\sf{→ 5.2 \times 12.5}$

$\sf \orange{→ 65}$

Since 8 triangles make up to an octagon we will multiply 65 to 8,

$\sf {→ 65 \times 8}$

$\sf \red{→520}$

$\therefore$ The area of octagon is 520 feet.

Now, volume of pool = $\sf{520 \times 3}$

$\sf \blue{→1560}$

$\therefore$ Volume of the pool is 1560 cubic feet.

It is given that each cubic foot takes 7.5 gallons to fill. So,

$\sf {→1560 \times 7.5}$

$\sf \fbox \green{→11700}$

$\therefore$ It takes 11700 gallons of water to fill the pool.

OPTION D (11700) is the right answer.