(1) A slice from a circular pizza of diameter 14 inches is cut in such a way, that the slice forms a sector of angle measuring 45 degree. Find the measure of area of the cut slice of the pizza. (in inches square)
(A) 17.5 (B) 18.25 (C) 19.2 (D) 19.75
Solution :
Given that,
The diameter of circular pizza is 14 inches.
Therefore the radious of circular pizza = 14/2 inches = 7 inches.
The Area of circular pizza = πr2 =π x 72
We know that the area of circular pizza = 360 Degree.
Therefore π x 72 = 360 Degree
Angle(in degree ) Area(in inches square)
360 π x 72
45 ?
The area of cut slice = 45 x π x 72 /360
= 19.2
The answer is (C) 19.2
(2) The area of a square and a rectangle are equal. If the length of the rectangle is 10 m more than the side of the square and it’s breadth is 8 m less than the side of the square, what is the perimeter of the rectangle?
(A) 164 m (B) 170 m (C) 160 m (D) 155 m
Solution : Let the length of the side of square is a m.
Area of the square = a2 .
So, length of rectangle (l) = (a + 10) and breadth (b) = (a – 8).
Area of the rectangle = (a + 10) x (a – 8)
According to the question,
a2=(a + 10) x (a – 8)
a2=a2 – 8a + 10a -80
10a – 8a -80 = a2 – a2
2a =80
a = 40
length of rectangle (l) = (40 + 10) = 50 m and breadth (b) = (40 – 8) = 32 m.
Therefore perimeter of rectangle = 2(l +b) =2(50 + 32)= 164 m.
Answer (A) 164 m
