Length of court $$ =30,5 \mathrm{~m} $$ Width of court $$ =15,25 \mathrm{~m} $$ Radius of semicircle $$ =4,9 \mathrm{~m} $$ Area of centre circle $$ =0,64 \mathrm{~m}^{2} $$ Area of circle $$ =\pi r^{2} $$ Circumference $$ =2 \pi r $$ $$ \pi=3,14 $$

Question

UpStudy AI · Accepted Answer

To solve the problem, we need to calculate various areas and circumferences based on the given dimensions of the court and the semicircle. Let's break it down step by step.

### Known Conditions
1. Length of court $$ L = 30.5 \, \text{m} $$
2. Width of court $$ W = 15.25 \, \text{m} $$
3. Radius of semicircle $$ r_s = 4.9 \, \text{m} $$
4. Area of center circle $$ A_c = 0.64 \, \text{m}^2 $$
5. Value of $$ \pi = 3.14 $$

### Step 1: Calculate the Area of the Semicircle
The area $$ A_s $$ of a semicircle is given by the formula:
$$
A_s = \frac{1}{2} \pi r_s^2
$$
Substituting the values:
$$
A_s = \frac{1}{2} \times 3.14 \times (4.9)^2
$$

### Step 2: Calculate the Circumference of the Semicircle
The circumference $$ C_s $$ of a semicircle is given by the formula:
$$
C_s = \pi r_s + 2r_s
$$
Substituting the values:
$$
C_s = 3.14 \times 4.9 + 2 \times 4.9
$$

### Step 3: Calculate the Area of the Rectangle (Court)
The area $$ A_r $$ of the rectangle (court) is given by:
$$
A_r = L \times W
$$
Substituting the values:
$$
A_r = 30.5 \times 15.25
$$

### Step 4: Calculate the Area of the Circle
The area $$ A_c $$ of a circle is given by the formula:
$$
A_c = \pi r^2
$$
We already have the area of the center circle, but if we need to calculate it for a different radius, we can use this formula.

Now, let's perform the calculations for the area of the semicircle, the circumference of the semicircle, and the area of the rectangle.

I'll calculate these values now.
Calculate the value by following steps:
- step0: Calculate:
  $$30.5\times 15.25$$
- step1: Multiply the numbers:
  $$465.125$$
Calculate or simplify the expression $$ 3.14 * 4.9 + 2 * 4.9 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$3.14\times 4.9+2\times 4.9$$
- step1: Multiply the numbers:
  $$15.386+2\times 4.9$$
- step2: Multiply the numbers:
  $$15.386+9.8$$
- step3: Add the numbers:
  $$25.186$$
Calculate or simplify the expression $$ (1/2) * 3.14 * (4.9)^2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{2}\times 3.14\times 4.9^{2}$$
- step1: Convert the expressions:
  $$\frac{1}{2}\times 3.14\left(\frac{49}{10}\right)^{2}$$
- step2: Multiply the terms:
  $$\frac{157}{100}\left(\frac{49}{10}\right)^{2}$$
- step3: Evaluate the power:
  $$\frac{157}{100}\times \frac{49^{2}}{10^{2}}$$
- step4: Multiply the fractions:
  $$\frac{157\times 49^{2}}{100\times 10^{2}}$$
- step5: Multiply:
  $$\frac{376957}{10^{4}}$$
- step6: Evaluate the power:
  $$\frac{376957}{10000}$$
### Step 1: Area of the Semicircle
The area of the semicircle is calculated as:
$$
A_s = \frac{1}{2} \times 3.14 \times (4.9)^2 \approx 37.6957 \, \text{m}^2
$$

### Step 2: Circumference of the Semicircle
The circumference of the semicircle is calculated as:
$$
C_s = 3.14 \times 4.9 + 2 \times 4.9 \approx 25.186 \, \text{m}
$$

### Step 3: Area of the Rectangle (Court)
The area of the rectangle (court) is calculated as:
$$
A_r = 30.5 \times 15.25 \approx 465.125 \, \text{m}^2
$$

### Summary of Results
- **Area of the Semicircle**: $$ A_s \approx 37.70 \, \text{m}^2 $$
- **Circumference of the Semicircle**: $$ C_s \approx 25.19 \, \text{m} $$
- **Area of the Court**: $$ A_r \approx 465.13 \, \text{m}^2 $$

If you need any further calculations or clarifications, feel free to ask!
The area of the semicircle is approximately 37.70 m², the circumference is approximately 25.19 m, and the area of the court is approximately 465.13 m².

Length of court \( =30,5 \mathrm{~m} \) Width of court \( =15,25 \mathrm{~m} \) Radius of semicircle \( =4,9 \mathrm{~m} \) Area of centre circle \( =0,64 \mathrm{~m}^{2} \) Area of circle \( =\pi r^{2} \) Circumference \( =2 \pi r \) \( \pi=3,14 \)

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Geometry Questions