Question

The Beta Club at the middle school is building a heart-shaped playground as a service project for the elementary school. The playground will be made of a square and two semicircles (see diagram). They will build the outline of the playground using 6-inch high framing then fill the space with rubber plavground filler. The Beta Club found a company that sells the filler at a price of $500 for 75 cubic feet. How much will it cost to fill the playground with rubber playground fill?

PLEASE I NEED HELP TO PASS THE SEMESTER!

Answer 1

`\Large \textsf{Read below}`

Explanation:

`\Large \text{$ \sf 6\:in = 0.5\:ft$}`

`\Large \text{$ \sf V = square\:area * height + circle\:area * height$}`

`\Large \text{$ \sf V = (45^2)\:.\:(0.5) + (3.14)\:.\:(22.5)^2\:.\:(0.5)$}`

`\Large \text{$ \sf V = (2,025)\:.\:(0.5) + (3.14)\:.\:(506.25)\:.\:(0.5)$}`

`\Large \text{$ \sf V = 1,012.5 + 794.81$}`

`\Large \text{$ \sf V = 1,807.31\:ft^3$}`

`\Large \text{$ \sf x = (1,807.31)/(75) * 500$}`

`\Large \boxed{\boxed{\text{$ \sf x = \$\:12,048.75$}}}`

Answer 2

$12051.44

Explanation:

Calculate the area of the square

The area of the square is simply the length squared:

Area of square = s²

= (45 ft)²

= 2025 ft²

Calculate the area of one semicircle:

The area of a semicircle is half the area of a full circle. The area of a circle is pi times the radius squared:

Area of circle = πr²

Area of semicircle = ½πr²

First, calculate the radius of the semicircle:

Radius = diameter / 2

= 45 ft / 2

= 22.5 ft

Now, calculate the area of the semicircle

Area of semicircle = ½ × π × ( 22.5 ft )²

≈ 795.2156404 ft²

Calculate the total area of the playground

The total area of the playground is the sum of the area of the square and the area of two semicircles:

Total area of playground = Area of square + 2 × Area of semicircle

= 2025 ft² + 2 × 795.2156404 ft²

≈ 3615.431281 ft²

Calculate the volume of the playground

The volume of the playground is the total area multiplied by the depth of the rubber filler:

Volume of playground = Total area × Depth

= 3615.431281 ft² × 6 in

= 3615.431281 ft² × 0.5 ft

≈ 1807.71564 ft³ (converting inches to feet)

Calculate the cost of filling the playground

The cost of filling the playground is the volume multiplied by the cost per cubic foot of the rubber filler:

Cost of filling playground = Volume × Cost per cubic foot

= 1807.71564 ft³ × $500 / 75 ft³

≈ $12051.4376

≈ $12051.44 ( in 2 d.p.)

Therefore, it will cost the Beta Club approximately $12051.44 to fill the heart-shaped playground with rubber filler.