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First question: Fig. 11.24

width of rectangle = 14 m.

both semicircles are of same size.

Diameter of each shaded semicircle = 14/2 = 7 m.

Radius of semicircle = 7/2 = 3.5 m

area of semicircle = Pi * 3.5² / 2 m²

combined area of two semicircles : Pi * 3.5² m²

Area of rectangle = 14 * 10 = 140 m²

unshaded area = 140 - Pi * 3.5² m²

calculate...

==========================

The cows are tied to some poles at the four corners.

So they can graze in the circular area that is allowed by the length of the rope. Length of the rope is equal to 70 /2 = 35 meters.

That is so because the cow at point A and the cow at point B can just meet at the center of the side AB. So two lengths of the rope make the length AB.

Area of sector around each corner

= 1/4 * area of the Circle of Radius 35 meters.

= Pi * 35² /4 square meters

Total area that is grazed by the four cows

= Pi * 35² /4 * 4 = Pi* 35² m²

total area of the square ABCD = 70² m²

area that remains ungrazed = 70² - Pi * 35² m²

calculate....

width of rectangle = 14 m.

both semicircles are of same size.

Diameter of each shaded semicircle = 14/2 = 7 m.

Radius of semicircle = 7/2 = 3.5 m

area of semicircle = Pi * 3.5² / 2 m²

combined area of two semicircles : Pi * 3.5² m²

Area of rectangle = 14 * 10 = 140 m²

unshaded area = 140 - Pi * 3.5² m²

calculate...

==========================

The cows are tied to some poles at the four corners.

So they can graze in the circular area that is allowed by the length of the rope. Length of the rope is equal to 70 /2 = 35 meters.

That is so because the cow at point A and the cow at point B can just meet at the center of the side AB. So two lengths of the rope make the length AB.

Area of sector around each corner

= 1/4 * area of the Circle of Radius 35 meters.

= Pi * 35² /4 square meters

Total area that is grazed by the four cows

= Pi * 35² /4 * 4 = Pi* 35² m²

total area of the square ABCD = 70² m²

area that remains ungrazed = 70² - Pi * 35² m²

calculate....