Question

A horse is tied to a peg at one corner of a square shaped grass

field of sides 15m by means of a 5m long rope.Answer the following questions:-

(a) What is the area of the grass field?

(i) 225m2 (ii) 225m (iii) 255m2 (iv) 15m

(b) The area of that part of the field in which the horse can graze.

(i) 19.625m2 (ii) 19.265m2 (iii) 19m2 (iv) 78.5 m2

(c) The grazing area if the rope were 10m long instead of 5m.

(i) 7.85m2 (ii) 785m2 (iii) 225m2 (iv) 78.5 m2

(d) The increase in grazing area if the rope were 10m long instead of 5m.

(i) 58.758m2 (ii) 58.875m2 (iii) 58m2 (iv) 78.5 m2

(e) The given problem is based on which concept?

(i) Coordinate geometry (ii) area related to circle

(iii) Circle (iv) None of these​

Answer 1

Given : A horse is tied to a peg at one corner of a square shaped grass field of sides 15m by means of a 5m long rope.

To find : What is the area of the grass field?

The area of that part of the field in which the horse can graze.

The grazing area if the rope were 10m long instead of 5m.

The increase in grazing area if the rope were 10m long instead of 5m.

The given problem is based on which concept

Solution:

area of the grass field = 15 x 15 = 225 m²

Square has 90 deg angles at sides

so Area covered by horse = (90/360) πr²

= (1/4)(3.14) * 5²

= 19.625 m²

The area of that part of the field in which the horse can graze. 19.625 m²

if rope = 10 cm then Area of Grazing = (1/4)(3.14) * 10² = 78.5 m²

increase in grazing area = 78.5 - 19.625 = 58.875 m²

The given problem is based on  area related to circle

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Answer 2

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58.875m²