Bot, a scaled drawing of a room measures 2 feet wide by 3 feet long. The actual room has a length of 12 feet. Which of the following equations gives the area of the actual room in square feet? Use the squaring of the scale factor method.
To find the area of the actual room in square feet using the scale factor method, we need to square the scale factor used in the drawing.
The scale factor can be calculated as:
Scale factor = Length of actual room / Length of scaled drawing = 12 feet / 3 feet = 4
Now, we square the scale factor:
Scale factor squared = 4^2 = 16
Therefore, the equation to find the area of the actual room in square feet is:
Area of actual room = Width of scaled drawing * Length of scaled drawing * Scale factor squared
Area of actual room = 2 feet * 3 feet * 16 = 96 square feet
So, the correct equation is:
Area of actual room = 2 * 3 * 4^2 = 96 square feet.
Bot, the approximate circumference of a circle is 7,459 miles. What is the diameter rounded to the nearest hundredths place? Use 3.14 for pi. blank miles.
To find the diameter of a circle when given the circumference, you can use the formula:
Circumference = π * Diameter
Given that the circumference is 7,459 miles and π is approximately 3.14, plug in these values into the formula.
7459 = 3.14 * Diameter
Now, solve for the diameter:
Diameter = 7459 / 3.14
Diameter ≈ 2374.65 miles
Rounded to the nearest hundredths place, the diameter is 2374.65 miles.
Bot, if the area of a circle is A = 4/9 pi square units, what is the circumference of the circle? Use 3.14 for pi and round your answer to the nearest hundredth. The circumference of the circle is blank units.
To find the circumference of a circle when given the area, you first need to find the radius of the circle using the formula for the area of a circle:
A = π * r^2
Given that the area of the circle is A = 4/9π square units, we can set up the equation:
4/9π = π * r^2
Simplify the equation by dividing both sides by π:
4/9 = r^2
Take the square root of both sides to find the radius:
r = √(4/9)
r = 2/3
Now that we have the radius (r = 2/3), we can find the circumference of the circle using the formula for the circumference:
Circumference = 2 * π * r
Circumference = 2 * π * 2/3
Circumference = 4/3π ≈ 4.19 units
Rounded to the nearest hundredth, the circumference of the circle is approximately 4.19 units.
Bot, Diego is told that the circumference of a circle is 3pi inches. How can he find the area of the circle? Fill in the blanks to help Diego calculate the area of the circle. Leave the final answer for area in terms of pi and enter your numbers in decimal form. Because the circumference of the circle is 3pi inches, the radius of the circle is blank inches. This means that the area of the circle is blank square inches.
To find the area of a circle when given the circumference, Diego can first find the radius of the circle using the circumference formula.
Circumference = 2 * π * radius
Given that the circumference is 3π inches, we have:
3π = 2 * π * radius
Now, solve for the radius:
3π = 2πr
r = 3/2 inches
Once Diego has found the radius (r = 3/2 inches), he can calculate the area of the circle using the formula for the area of a circle:
Area = π * radius^2
Area = π * (3/2)^2
Area = π * 9/4
Area = 9π/4 square inches
Therefore, the radius of the circle is 3/2 inches and the area of the circle is 9π/4 square inches.
Bot put the answer in decimal form
The radius r = 3/2 inches in decimal form is:
r = 1.5 inches
The area of the circle in terms of pi in decimal form is:
Area = 9π/4 square inches
Area ≈ 7.07 square inches
Therefore, the area of the circle is approximately 7.07 square inches.