Area - Study Mode

[#186] A small ring of negligible thickness and radius 2 cm moves on a bigger rung of radius 10 cm. How many rotations will the small ring take on the bigger ring to make a complete round ?
Correct Answer

(A) 5

Explanation

Solution: Required number of rotations : $$eqalign{
& = frac{{{ ext{Circumference of bigger ring}}}}{{{ ext{Circumference of smaller ring}}}} cr
& = frac{{2 imes pi imes 10}}{{2 imes pi imes 2}} cr
& = 5 cr} $$

[#187] What will be the area of a semi-circle whose perimeter is 36 cm ?
Correct Answer

154 cm 2

Explanation

Solution: Given : $$eqalign{
& pi R + 2R = 36 cr
& Leftrightarrow left( {pi + 2}
ight)R = 36 cr
& Leftrightarrow R = frac{{36}}{{left( {frac{{22}}{7} + 2}
ight)}}cm cr
& Leftrightarrow R = 7,cm cr} $$ Required area : $$eqalign{
& = frac{{pi {R^2}}}{2} cr
& = left( {frac{{22}}{7} imes frac{{7 imes 7}}{2}}
ight)c{m^2} cr
& = 77,c{m^2} cr} $$

[#188] The area of a circle of radius 5 is numerically what percent of its circumference ?
Correct Answer

(D) 250%

Explanation

Solution: $$eqalign{
& { ext{Required % }} = left[ {frac{{pi imes {{left( 5
ight)}^2}}}{{2pi imes 5}} imes 100}
ight]\% cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, = 250\% cr} $$

[#189] A wire can be bent in the form of a circle of radius 56 cm. If it is bent in the form of a square, then its area will be :
Correct Answer

(C) 7744 cm 2

Explanation

Solution: Length of wire : $$eqalign{
& = 2pi imes R cr
& = left( {2 imes frac{{22}}{7} imes 56}
ight)cm cr
& = 352,cm cr} $$ Side of the square : $$eqalign{
& = frac{{352}}{4},cm cr
& = 88,cm cr} $$ Area of the square : $$eqalign{
& = left( {88 imes 88}
ight)c{m^2} cr
& = 7744,c{m^2} cr} $$

[#190] The circumference of the front wheel of a cart is 40 ft long and that of the back wheel is 48 ft long. What is the distance travelled by the cart, when the front wheel has done five more revolutions than the rear wheel ?
Correct Answer

(C) 1200 ft

Explanation

Solution: Let the rear wheel make x revolutions Then, the front wheel makes (x + 5) revolutions (x + 5) × 40 = 48x ⇒ 8x = 200 ⇒ x = 25 Distance travelled by the cart : = (48 × 25) ft = 1200 ft