A circle is cut from a square piece of cloth, as shown:
A square, one side labeled as 42 inches has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.
How many square inches of cloth are cut from the square? (π = 3.14) (1 point)
131.88 in2
168.00 in2
1,384.74 in2
1,764.00 in2
To find the area of the cloth cut from the square, we need to calculate the area of the square and subtract the area of the circle.
Since the side length of the square is given as 42 inches, the area of the square is (42 inches) * (42 inches) = 1,764 square inches.
The radius of the circle is equal to half of the side length of the square, so the radius of the circle is (42 inches)/2 = 21 inches.
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. Plugging in the given values, we have A = 3.14 * (21 inches)^2 = 1,384.74 square inches.
To find the area of the cloth cut from the square, we subtract the area of the circle from the area of the square: 1,764 square inches - 1,384.74 square inches = 379.26 square inches.
Thus, the correct answer is not listed.
A running track in the shape of an oval is shown. The ends of the track form semicircles.
A running track is shown. The left and right edges of the track are identical curves. The top and bottom edges of the track are straight lines. The track has width 62 m and length of one straight edge 100 m
What is the perimeter of the inside of the track? (π = 3.14) (1 point)
162.00 m
324.00 m
394.68 m
589.36 m
To find the perimeter of the inside of the track, we need to calculate the sum of the lengths of the two straight edges and the two semicircles.
The length of one straight edge is given as 100 m.
The width of the track is given as 62 m.
The length of the other straight edge is also 100 m.
The formula for the perimeter of a semicircle is P = πr + 2r, where P is the perimeter and r is the radius.
The radius of the semicircle is equal to half of the width of the track, so the radius is 62 m / 2 = 31 m.
The length of a semicircle is half of the circumference of a circle, so the length of one semicircle is (π * 2 * 31 m) / 2 = 3.14 * 31 m = 97.34 m.
To find the perimeter of the inside of the track, we add up the lengths of the straight edges and the semicircles: 100 m + 97.34 m + 100 m + 97.34 m = 394.68 m.
Thus, the perimeter of the inside of the track is 394.68 m.
The correct answer is 394.68 m.