Question

10.) A horse is placed for grazing inside a rectangular
field 40 m by 36 m and is tethered to one corner
by a rope 14 m long. Over how much area can it
graze?​

Answer 1

Answer:

• The horse can graze over a area of 154 m².

Step-by-step explanation:

Given that:

• A horse is placed for grazing inside a rectangular field.It is tethered to one corner by a rope of 14 m long.

To Find:

• Area which can grazed by the horse.

Concept:

Here we have been given that, a horse is tied on the corner of a rectangular field with a rope of length 14 m. We have to find the area grazed by the horse.

How to do:

The area which the horse can graze will be 1/4th of the area of a circle with the radius 14 m.

Solution:

As we know that,

Area of a circle = (πr²) sq. units

Where,

• r = Radius

So, area grazed by the horse:

$\sf{\longmapsto \dfrac{1}{4}\times\left(\pi r^2\right)}$

Here,

• r = OA = 14 m

Substituting the values,

$\sf{\longmapsto \dfrac{1}{4}\times\left(\dfrac{22}{7} \times14^2\right)}$

$\sf{\longmapsto \dfrac{1}{4}\times\left(\dfrac{22}{7}\times14\times14\right)}$

Reducing the numbers,

$\sf{\longmapsto \dfrac{1}{4}\times\left(22 \times2\times14\right)}$

Multiplying,

$\sf{\longmapsto \dfrac{1}{4}\times616}$

$\sf{\longmapsto \dfrac{616}{4}}$

Dividing,

$\sf{\longmapsto 154}$

Hence,

Area grazed by the horse = 154 m²