Area, General Mathematics

Question: The number of rounds that a wheel of diameter` 7/11` m will make in going 4 km is :
A
1000

B
1500

C
1700

D
2000

Note: Distance moved in 1 revolution `= (2 xx 22/7 xx 7/22) m.` `= 2 m.` Number of revolutions in going 4 km `= ((4 xx 1000)/2)` `= 2000`
1. Report
Question: If the radius of a circle is decreased by 50%, its area will decease by :
A
25%

B
50%

C
75%

D
None

Note: Let original radius = R. New radius `= 50/100 R` `= R/2.` Original area `π R^2` & New area `= π (R/2)^2` `= (π R^2)/4.` Decrease in area `= ((3 π R^2)/4 xx 1/( π R^2) xx 100)% `= 75%`
1. Report
Question: If the diameter of a circle is decreased by 100%, its area is increased by :
A
100%

B
200%

C
300%

D
400%

Note: Let original radius = R, New Radius `= 200/100 R = 2 R`. :. Original area` = π R^2`, New area `= π (2R)^2` `= 4 π R^2` :. Increase %`= ((3 π R^2)/(π R^2) xx 100) %` `= 300 %.`
1. Report
Question: If the circumference of a circle is increased by 50%, then its area will be increased by :
A
50%

B
100%

C
125%

D
225%

Note: Let original radius = r. Then, circumference = 2 π r and area `= π r^2` New circumference `= (150/100 xx 2 π r)` `= 3 π r` Let radius now be R. `2 π R = 3 π r => R = 3r/2.` New area` = π R^2 = π ((9r^2)/4)` `= (9π r^2)/4` Increase in area `= ((9π r^2)/4 - π r^2)` `= (5 π r^2)/4.` :. Increase %` = ((5 π r^2)/4 xx 1/(π R^2) xx 100) %` `= 125%`
1. Report
Question: The area of a circular field is 13.86 hectares. The cost of fencing it at the rate of 40 paise per metre is :
A
`Rs. 554.40`

B
`Rs. 528`

C
`Rs. 396`

D
`Rs. 648`

Note: Area` = (13.86 xx 100000) sq.m` `= 138600 m^2.` `π R^2 = 138600 or R^2` `= (138600 xx 7/22) => R` `= 210 m.` Circumference` = 2 π R = (2 xx 22/7 xx 210) m` `= 1320 m.` cost of fencing` = Rs. (1320 xx 40/100)` `= Rs. 528`
1. Report
Question: The area of the largest circle that can be drawn inside a square of side 14 cm in length, is :
A
`154 cm^2`

B
`84 cm^2`

C
`204 cm^2`

D
None of these

Note: Radius of the required circle = 7 cm. :. Its area` = (22/7 xx 7 xx 7) cm^2` `= 154 cm^2`
1. Report
Question: The area of the largest circle that can be drawn inside a rectangle with sides 7 metres by 3.5 metres is :
A
`38 1/2 m^2`

B
`9 5/8 m^2`

C
`77 m^2`

D
None of these

Note: Radius of required circle` = 7/4 cm` :. Its area` = (22/7 xx 7/4 xx 7/4) cm^2` `= 9 5/8 cm^2`
1. Report
Question: The area of largest possible square inscribed in a circle of unit radius (in sq. units) is :
A
2

B
π

C
`2sqrt(2) π`

D
`4sqrt(2) π`

Note: Diagonal of square = Diameter of circle = 2 units. :. Area of the square` = 1/2 xx (diagonal)^2` `= (1/2 xx 2 xx 2) = 2 sq.` units
1. Report
Question: The ratio of the areas of the incircle and circumcircle of a square is :
A
`1 : sqrt(2)`

B
`1 : sqrt(3)`

C
`1 : 4`

D
`1 : 2`

Note: Let the side of the square be x. Then, its diagonal `= sqrt(2) x.` :. Radius of incircle` = x/2` & radius of circumcircle `= sqrt(2x)/2 = x/sqrt(2)` :. Required ratio `= ((π x^2)/4 : (π x^2)/2)` `= 1/4 : 1/2` `= 1 : 2`.
1. Report
Question: The ratio of the ares of the incircle and circumcircle of an equilateral triangle is :
A
`1 : 2`

B
`1 : 2`

C
`1 : 4`

D
`1: 9`

Note: Let radius of incircle be r. Then, radius of circumcircle = 2r. :. Required ratio`= (π r^2)/((π (2r)^2` `= 1/4`
1. Report

First Prev 7 8 9 10 Next Last

Question: The number of rounds that a wheel of diameter` 7/11` m will make in going 4 km is :

Question: If the radius of a circle is decreased by 50%, its area will decease by :

Question: If the diameter of a circle is decreased by 100%, its area is increased by :

Question: If the circumference of a circle is increased by 50%, then its area will be increased by :

Question: The area of a circular field is 13.86 hectares. The cost of fencing it at the rate of 40 paise per metre is :

Question: The area of the largest circle that can be drawn inside a square of side 14 cm in length, is :

Question: The area of the largest circle that can be drawn inside a rectangle with sides 7 metres by 3.5 metres is :

Question: The area of largest possible square inscribed in a circle of unit radius (in sq. units) is :

Question: The ratio of the areas of the incircle and circumcircle of a square is :

Question: The ratio of the ares of the incircle and circumcircle of an equilateral triangle is :