The square surface cover shown in the figure is 10.16 centimeters on each side. The knockout in the center of the cover has a diameter of 1.27 centimeters. Find the area of the cover to the nearest hundredth centimeter.

Question
Circles
asked 2020-11-08
The square surface cover shown in the figure is 10.16 centimeters on each side. The knockout in the center of the cover has a diameter of 1.27 centimeters. Find the area of the cover to the nearest hundredth centimeter.

Answers (1)

2020-11-09
The area of the cover is the area of the square minus the area of the circle: Acover=Asquare-Acircle Acover=\(\displaystyle{8}^{{2}}-\frac{{π{d}^{{2}}}}{{4}}\)
Substitute s=10.16 cm and d=1.27 cm: Acover=\(\displaystyle{10.16}^{{2}}-{\left(π\frac{{\left({1.27}\right)}^{{2}}}{{4}}\right.}\)
Use a calculator and round to the nearest hundredth cm (2 decimal places):
Acover≈101.96 cm
0

Relevant Questions

asked 2020-12-17
Carlos is spreading mulch in a circle on top of an area where he has planted some seeds. He has enough mulch to cover an area that is 12.5 square feet. How much rubber edging does Carlos need to encircle the mulch that will cover the seeds?
asked 2020-12-02
Determine the length of wire in feet in a coil of 65 turns if the average diameter of the coil is 27.20 inches.
asked 2021-01-15
Find the perimeter of the semicircular region. Round to the nearest hundredth.
asked 2021-02-21
A circle has a circumference of \(\displaystyle{48}π\) centimeters. If the radius of the circle is multiplied by 9, what is the circumference of the new circle?
asked 2021-02-24
The volume of a sphere is given bby the equation \(\displaystyle{V}\ =\ {\frac{{{1}}}{{{6}\sqrt{{\pi}}}}}\ {S}^{{\frac{{3}}{{2}}}}\), where S is the surface area of the sphere. Find the volume of a sphere, to the nearest cubic meter, that has a surface area of 60 square meter. Use 3.14 for \(\displaystyle\pi\).
asked 2021-01-31
A rotational axis is directed perpendicular to the plane of asquare and is located as shown in the drawing. Two forces,1and 2,are applied to diagonally opposite corners, and act along the sidesof the square, first as shown in part a and then as shown inpart b of the drawing. In each case the net torque producedby the forces is zero. The square is one meter on a side, and themagnitude of 2 is5 times that of 1.Find the distances a and b that locate the axis. Notethat a and b are not drawn to scale.
a=___m
b=___m
asked 2021-01-10
A water sprinkler sprays water on a lawn over a distance of 25 feet and rotates through an angle of \(130^(circ)\). Find the area of the lawn watered by the sprinkler.
asked 2021-02-06
Find the area of sector AOB if the radius of circle O is 12 cm. Give the answer in terms of π.
asked 2021-03-09
Identify the center and ydius of each. \(\displaystyle{4}{x}^{{12}}−{16}{x}+{y}^{{2}}−{8}{y}={1}\)
asked 2020-10-23
1. Find each of the requested values for a population with a mean of \(? = 40\), and a standard deviation of \(? = 8\) A. What is the z-score corresponding to \(X = 52?\) B. What is the X value corresponding to \(z = - 0.50?\) C. If all of the scores in the population are transformed into z-scores, what will be the values for the mean and standard deviation for the complete set of z-scores? D. What is the z-score corresponding to a sample mean of \(M=42\) for a sample of \(n = 4\) scores? E. What is the z-scores corresponding to a sample mean of \(M= 42\) for a sample of \(n = 6\) scores? 2. True or false: a. All normal distributions are symmetrical b. All normal distributions have a mean of 1.0 c. All normal distributions have a standard deviation of 1.0 d. The total area under the curve of all normal distributions is equal to 1 3. Interpret the location, direction, and distance (near or far) of the following zscores: \(a. -2.00 b. 1.25 c. 3.50 d. -0.34\) 4. You are part of a trivia team and have tracked your team’s performance since you started playing, so you know that your scores are normally distributed with \(\mu = 78\) and \(\sigma = 12\). Recently, a new person joined the team, and you think the scores have gotten better. Use hypothesis testing to see if the average score has improved based on the following 8 weeks’ worth of score data: \(82, 74, 62, 68, 79, 94, 90, 81, 80\). 5. You get hired as a server at a local restaurant, and the manager tells you that servers’ tips are $42 on average but vary about \($12 (\mu = 42, \sigma = 12)\). You decide to track your tips to see if you make a different amount, but because this is your first job as a server, you don’t know if you will make more or less in tips. After working 16 shifts, you find that your average nightly amount is $44.50 from tips. Test for a difference between this value and the population mean at the \(\alpha = 0.05\) level of significance.
...