Long Answer Type Questions :-
1. A wire when bent in the form of a square encloses an area of 484 cm². If the same wire is bent in the form of a circle, find the area of the circle.
2. Two crossroads, each of width 4 m, runs at right angles through the centre of a rectangular park of length 70 m and breadth 45 m and parallel to the sides of the rectangle. Find the area of the road.
3. The circumference of two circles are in the ratio 8 : 6. Find the ratio of their areas.
4. A rectangular piece of a canvas measures 35 m by 18 m. A triangular piece with base 18 m and height 12 m is cut from the canvas. Find the area of the remaining piece.
5. A mirror of length 30 cm and width 25 cm is to be framed with a 4 cm wide frame. Find the area of the frame required. Also find the cost of framing at the rate of ₹ 25 per cm².
Answers
Solution :
1. A wire when bent in the form of a square encloses an area of 484 cm² .
Let the side of the wire forming the square be x cm .
Thus , area of the square becomes :
=> x² = 484
=> x = 22 cm .
Perimeter of the square :
=> 4x
=> 88 cm .
Thus the entire length of the wire becomes 88 cm .
It is now bent in the form of a circle .
Let us assume that the circle has a radius r .
Circumference :
2 π r = 88 cm
2× 22/7 r = 88
=> r = 14 cm
Area = π r²
=> 22/7 × 14 × 14
=> 44 × 14
=> 616 cm² .
2. The rectangle has a length of 70 m and a breadth of 45 m .
The width of the roads is 4 m .
Answer:
1.Area of the square=484cm
2
∴ Side of the square =
484
=22cm
⇒ Perimeter of the square =4×22=88cm
∵ (Circumference of the circle) = (perimeter of the square)
⇒2πr=88
⇒2×
7
22
×r=88
∴r=
2×22
88×7
=14cm
∴ Area of the circle =πr
2
=
7
22
×14×14cm
2
=616cm
2.Answer
width =5 m
length of first parallel road 70 m
area of first road 70×5=350 sq.m
length of second road 45 m
area of second road =45×5=225 sq.m
area of the common part of cross road with 5 m width that lies at the
center of the park 5×5 = 225 sq.m
area of roads = area of first road +area of second cross road−common area
=(350+225)−25
=575−25
=550sqm
cost of the construction per sq.m =Rs.105
total cost =550×105=Rs 57750