Find the ratio of the areas of the incircle and circumcircle of a square. 1:1 1:

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Question
Find the ratio of the areas of the incircle and circumcircle of a square.
Options
A. 1:1
B. 1:2
C. 1:3
D. 1:4

Correct Answer

1:2

Explanation

Let the side of the square be x. Then, its diagonal = $\sqrt{2 x^{2}} = \sqrt{2 x}$

Radius of incircle = $\frac{x}{2}$

Radius of circum circle= $\sqrt{2} � \frac{x}{2} = \frac{x}{\sqrt{2}}$

Required ratio = $\frac{{?x}^{2}}{4} : \frac{{?x}^{2}}{2} = \frac{1}{4} : \frac{1}{2} = 1 : 2$

Area problems

Search Results

1. A room is 15 feet long and 12 feet broad. A mat has to be placed on the floor of the room leaving 1.5 feet space from the walls. What will be the cost of the mat at the rate of Rs. 3.50 per squire feet?
Options
A. 378
B. 472.5
C. 496
D. 630

2. The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?
Options
A. 40
B. 20
C. 30
D. none of these

3. The difference between two parallel sides of a trapezium is 4 cm. perpendicular distance between them is 19 cm. If the area of the trapezium is 475 find the lengths of the parallel sides.
Options
A. 27 and 23
B. 24 and 23
C. 25 and 23
D. 22 and 23

4. The sides of a right-angled triangle are 12 cm, 16 cm, 20 cm respectively. A new right angle Δ is made by joining the midpoints of all the sides. This process continues for infinite then calculate the sum of the areas of all the triangles so made.
Options
A. 312 sq.cm
B. 128 sq.cm
C. 412 sq.cm
D. 246 sq.cm

5. The area of the circle is 220 sq.m, the area of the square inscribed in a circle will be
Options
A. 49
B. 70
C. 140
D. 150

6. The perimeter of a rectangle whose length is 6 m more than its breadth is 84 m. What will be the area of the rectangle?
Options
A. 333 sq.mts
B. 330 sq.mts
C. 362 sq.mts
D. 432 sq.mts

7. What is the least number of squares tiles required to pave the floor of a room 15.17 m long and 9.02 m broad?
Options
A. 814
B. 714
C. 614
D. 713

8. A rectangular plot measuring 90 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed?
Options
A. 65m
B. 45m
C. 55m
D. 56m

9. The length and the breadth of rectangular field are in the ratio of 8 : 7. If charges of the painting the boundary of rectangle is at Rs. 10 per meter is Rs. 3000. What is the area of rectangular plot?
Options
A. 5600 sq.m
B. 1400 sq. m
C. 4400 sq.m
D. 3600 sq.m

10. If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.
Options
A. 20
B. 30
C. 40
D. 50

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