Alex then paints the face of the clock with white paint. It has a diameter of 14 inches. What is the area of the clock face?
Next, Alex glued a band of metal around the circumference of the clock. What is the length of the metal band?
Well, let's start with the area of the clock face. To find it, we'll use the formula for the area of a circle, which is π multiplied by the radius squared. The diameter of the clock is 14 inches, so the radius would be half of that, which is 7 inches. Now we can calculate the area.
A = π * r^2
A = π * 7^2
A ≈ 3.14 * 49
A ≈ 153.86 square inches
So, the area of the clock face is approximately 153.86 square inches. Now, onto the metal band. To find its length, we need to calculate the circumference of the clock, which can be found using the formula 2πr. The radius is still 7 inches, so we can plug that into the equation.
C = 2πr
C = 2 * 3.14 * 7
C ≈ 43.96 inches
Therefore, the length of the metal band is approximately 43.96 inches. Just make sure Alex didn't glue it on too tightly -- we don't want the clock to feel choked!
To find the area of the clock face, we need to calculate the area of a circle. The formula for the area of a circle is given by:
A = π * r^2
Given that the diameter of the clock is 14 inches, we can determine the radius (r) by dividing the diameter by 2:
r = 14 inches / 2 = 7 inches
Substituting this value into the formula, we have:
A = π * (7 inches)^2
Now, to find the area, we need to multiply π by the square of the radius:
A = 3.14 * 49 square inches
A ≈ 153.86 square inches
Therefore, the area of the clock face is approximately 153.86 square inches.
Next, to find the length of the metal band glued around the circumference of the clock, we need to calculate the circumference. The formula for the circumference of a circle is given by:
C = 2 * π * r
Using the radius we calculated earlier (r = 7 inches), we can substitute it into the formula:
C = 2 * 3.14 * 7 inches
C ≈ 43.96 inches
Therefore, the length of the metal band is approximately 43.96 inches.
To find the area of the clock face, we can use the formula for the area of a circle: A = πr^2, where A is the area, and r is the radius. First, let's find the radius of the clock face by dividing the diameter by 2. The diameter is given as 14 inches, so the radius would be 14 divided by 2, which is 7 inches.
To calculate the area, substitute the value of the radius into the formula: A = π(7^2). Since the radius is 7, we can square it to get 49. Now, multiplying it by π (pi, approximately 3.14159), we get the answer. Therefore, the area of the clock face is approximately 153.94 square inches.
For the length of the metal band glued around the circumference of the clock, we need the circumference of the circle. The circumference of a circle can be found using the formula C = 2πr, where C is the circumference and r is the radius.
Substituting the radius value of 7 inches into the formula, we get C = 2π(7). Multiplying 2 by π and then by 7, we get the answer. Therefore, the length of the metal band is approximately 43.98 inches.
A = pi * r^2
A = 3.14 * 7^2
C = pi * d
C = 3.14 * 14