The radius of a circular field is equal to the side of a square field whose perimeter is 784 feet. What is the area of the circular field?
(a) 107914 sq.ft.
(b) 120736 sq.ft.
(c) 107362 sq.ft.
(d) 127306 sq.ft.
(e) None of these
Solution: (b)
Radius of the circular field = side of the square = \(\displaystyle \frac{{784}}{4}=196 feet\)
Area of the circular field =\(\displaystyle \pi \times {{r}^{2}}=\frac{{22}}{7}\times 196\times 196=120736 sq.ft\)
The area of a square is thrice the area of a rectangle. If the area of the square is 225sq cm and the length of the rectangle is 15 cm, what is the difference between the breadth of the rectangle and the side of the square?
(a) 8 cm
(b) 10 cm
(c) 12 cm
(d) 16 cm
(e) None of these
Solution: (b)
Area of rectangle = \(\displaystyle \frac{{225}}{3}=75sqcm\)
Breadth of rectangle = \(\displaystyle \frac{{Area}}{{Length}}=\frac{{75}}{{15}}=5cm\)
Side of the square = \(\displaystyle \sqrt{{Area}}=\sqrt{{225}}=15cm\)
Required difference = (15 – 5) 10 cm
A rectangular field has its length and breadth in the ratio of 6 : 5 respectively. A man riding a bicycle, completes one lap of this field along its perimeter at the speed of 19.8 km/hr in 2 minutes. What is the area of the field?
Therefore, Area of the field = \(\displaystyle 6x\times 5x\) \(\displaystyle 30{{x}^{2}}\)
= \(\displaystyle 30\times 30\times 30=27000sqm\)
The perimeter of a square is thrice the perimeter of a rectangle. If the perimeter of the square is 84 cm and the length of the rectangle is 8 cm, what is the difference between the breadth of the rectangle and the side of the square?
(a) 15 cm
(b) 19 cm
(c) 10 cm
(d) 8 cm
(e) None of these
Solution: (a)
Perimeter of the square = 84 cm
Perimeter of the rectangle = 28 cm
Perimeter of the rectangle = 2(1 + b)
or, 2(8 + b) = 28 cm
or, b = 14 – 8 = 6 cm
Breadth of the rectangle = 6 cm
Side of the square = \(\displaystyle \frac{{84}}{4}=21cm\)
Difference = 21 – 6 = 15 cm
The perimeter of a square is twice the perimeter of a rectangle. If the perimeter of the square is 72 cm and the Iength of the rectangle is 12 cm. what is the difference between the breadth of the rectangle and the side of the square?
(a) 9 cm
(b) 12 cm
(c) 18 cm
(d) 3cm
(e) None of these
Solution: (b)
Perimeter of square = 72 cm
Perimeter of rectangle = \(\displaystyle \frac{{72}}{2}=36cm\)
Therefore, Side of the square = \(\displaystyle \frac{{72}}{4}=18cm\)
