Area - Study Mode

[#136] A circular road runs around a circular garden. If the difference between the circumference of the outer circle and the inner circle is 44 m, the width of the road is :
Correct Answer

(C) 7 m

Explanation

Solution: Let the radii of the outer and inner circle be R and r respectively Then, $$eqalign{
& 2pi R - 2pi r = 44 cr
& Rightarrow 2pi left( {R - r}
ight) = 44 cr
& Rightarrow left( {R - r}
ight) = frac{{44 imes 7}}{{22 imes 2}} cr
& Rightarrow left( {R - r}
ight) = 7 cr} $$

[#137] The area of the greatest circle which can be inscribed in a square whose perimeter is 120 cm, is :
Correct Answer

(D) $$frac{{22}}{7} imes {left( {15} ight)^2}c{m^2}$$

Explanation

Solution: Side of the square : $$eqalign{
& = frac{{120}}{4}cm cr
& = 30,cm cr} $$ Radius of the required circle : $$eqalign{
& = left( {frac{1}{2} imes 30}
ight)cm cr
& = 15,cm cr
& = pi imes {r^2} cr
& = left[ {frac{{22}}{7} imes {{left( {15}
ight)}^2}}
ight]c{m^2} cr} $$

[#138] If the area of the trapezium whose parallel sides are 6 cm and 10 cm is 32 sq. cm, then the distance between the parallel sides is :
Correct Answer

(B) 4 cm

Explanation

Solution: Let the required distance be x cm Then, $$eqalign{
& Rightarrow frac{1}{2} imes left( {6 + 10}
ight) imes x = 32 cr
& Rightarrow x = 4,cm cr} $$

[#139] The radius of a circle is 20% more than the height of a right-angled triangle. The base of the triangle is 36 cm. If the area of triangle and circle be equal, what will be area of circle ?
Correct Answer

(A) 72 cm 2

Explanation

Solution: Let the height of the triangle be x cm Then, radius of the circle = (120% of x) cm = $$left( {frac{{6x}}{5}}
ight)$$ cm $$eqalign{
& herefore frac{1}{2} imes 36 imes x = frac{{22}}{7} imes frac{{6x}}{5} imes frac{{6x}}{5} cr
& Rightarrow x = left( {frac{{18 imes 7 imes 5 imes 5}}{{22 imes 6 imes 6}}}
ight)cm cr} $$ So, radius of the circle : $$eqalign{
& = left[ {frac{6}{5} imes left( {frac{{18 imes 7 imes 5 imes 5}}{{22 imes 6 imes 6}}}
ight)}
ight]cm cr
& = left( {frac{{105}}{{22}}}
ight)cm cr} $$ ∴ Area of the circle : $$eqalign{
& = left( {frac{{22}}{7} imes frac{{105}}{{22}} imes frac{{105}}{{22}}}
ight)c{m^2} cr
& = left( {frac{{1575}}{{22}}}
ight)c{m^2} cr
& = 71.6,c{m^2} approx 72,c{m^2} cr} $$

[#140] The radius of the wheel of a vehicle is 70 cm. The wheel makes 10 revolutions in 5 seconds. The speed of the vehicle is :
Correct Answer

(B) 31.68 km/hr

Explanation

Solution: Distance covered in 5 sec : $$eqalign{
& = left( {2 imes frac{{22}}{7} imes 70 imes 10}
ight)cm cr
& = 4400,cm cr
& = 44,m cr} $$ Distance covered in 1 sec : $$eqalign{
& = left( {frac{{44}}{5}}
ight)m cr
& = 8.8,m cr} $$ ∴ Speed : $$eqalign{
& = 8.8,m/sec cr
& = left( {8.8 imes frac{{18}}{5}}
ight)km/hr cr
& = 31.68,km/hr cr} $$