Area - Study Mode

[#146] A piece of wire when bent to from a circle will have a radius of 84 cm. If the wire is bent to form a square, the length of a side of the square is :
Correct Answer

(C) 132 cm

Explanation

Solution: Given length of the piece of wire = 84 cm Length of the piece of wire = Circumference of circle $$eqalign{
& = 2pi r cr
& = 2 imes frac{{22}}{7} imes 84 cr
& = 528,cm cr} $$ Length of each side of square = a ∴ Perimeter of square = 4a = 528 cm ∴ Side of square = $$frac{{528}}{4}$$ = 132 cm

[#147] A carpenter is designing a table. The table will be in the form of a rectangle whose length is 4 feet more than its width. How long should the table be if the carpenter wants the area of the table to be 45 sq. ft ?
Correct Answer

(B) 9 ft

Explanation

Solution: Let the width of the table be x feet. Then, length of the table = (x + 4) ft $$eqalign{
& herefore xleft( {x + 4}
ight) = 45 cr
& Rightarrow {x^2} + 4x - 45 = 0 cr
& Rightarrow {x^2} + 9x - 5x - 45 = 0 cr
& Rightarrow xleft( {x + 9}
ight) - 5left( {x + 9}
ight) = 0 cr
& Rightarrow left( {x + 9}
ight)left( {x - 5}
ight) = 0 cr
& Rightarrow x = 5 cr} $$ Hence, length of the table = (5 + 4) = 9 feet

[#148] The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
Correct Answer

(B) 153600 m 2

Explanation

Solution: Perimeter = Distance covered in 8 min. Perimeter = $$left( {frac{{12000}}{{60}} imes 8}
ight){ ext{m}}$$ Perimeter = 1600 m Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160 Therefore Length = 480 m and Breadth = 320 m Therefore Area = (480 x 320) m 2 = 153600 m 2

[#149] An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
Correct Answer

(D) 4.04%

Explanation

Solution: 100 cm is read as 102 cm. ∴ A 1 = (100 x 100) cm 2 and A 2 (102 x 102) cm 2 (A 2 - A 1 ) = [(102) 2 - (100) 2 ] = (102 + 100) x (102 - 100) = 404 cm 2 ∴ Percentage error $$eqalign{
& = left( {frac{{404}}{{100 imes 100}} imes 100}
ight)\% cr
& = 4.04\% cr} $$

[#150] The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
Correct Answer

(B) 18 cm

Explanation

Solution: $$eqalign{
& frac{{2left( {l + b}
ight)}}{b} = frac{5}{1} cr
& Rightarrow 2l + 2b = 5b cr
& Rightarrow 3b = 2l cr
& b = frac{2}{3}l cr
& { ext{Then,}} cr
& { ext{Area = }}216,c{m^2} cr
& Rightarrow l imes b = 216 cr
& Rightarrow l imes frac{2}{3}l = 216 cr
& Rightarrow {l^2} = 324 cr
& l = 18,cm cr} $$