Question

8. A cow is tied with a rope in the centre of a circular lawn of diameter 28 cm. If the length of the rope 7 cm, find the area of the lawn which the cow can graze. Also find the remaining area of the lawn. Ans is Area of grazed portion =154 cm² ,Area of ungrazed portion=462 cm² step by step​

Answer 1

Question :

A cow is tied with a rope in the centre of a circular lawn of diameter 28 cm. If the length of the rope 7 cm, find the area of the lawn which the cow can graze. Also find the remaining area of the lawn. Ans is Area of grazed portion =154 cm² ,Area of ungrazed portion=462 cm² step by step

Answer :

$\sf\pink{Given}$

• Diameter of the circular lawn is 28 cm .

• Length of the rope is 7 cm .

$\sf\pink{To\:find}$

• Area the cow can graze

• Reaming area of the lawn

Area the cow can graze is equal to the smaller circle formed inside the lawn by the rope which acts as it's radius .

$\bf\red{Area\:of\:smaller\:circle = \pi{r}^{2}}$

• r is 7 cm

$\bf\red{Area\:of\:smaller\:circle = \dfrac{22}{7}\times {7}^{2}}$

$\bf\red{Area\:of\:smaller\:circle = \dfrac{22}{7}\times 49}$

$\bf\red{Area\:of\:smaller\:circle = 22\times 7}$

$\bf\red{Area\:of\:smaller\:circle = 154 }$

• Area the cow can graze is 154 cm²

$\bf\purple{Area\:of\:lawn = \pi {r}^{2}}$

• diameter is 28 so radius will be half of it that is 14 cm

$\bf\purple{Area\:of\:lawn = \dfrac{22}{7}\times {14}^{2}}$

$\bf\purple{Area\:of\:lawn = \dfrac{22}{7}\times 14\times 14}$

$\bf\purple{Area\:of\:lawn = 22\times 2\times 14}$

$\bf\purple{Area\:of\:lawn = 44\times 14}$

$\bf\purple{Area\:of\:lawn = 616}$

• Therefore area of lawn is 616 cm²

$\bf\pink{Remaining\:Area = Area\:of\:lawn - Area\:of\: grazing}$

$\bf\pink{Remaining\:Area = 616 - 164}$

$\bf\pink{Remaining\:Area = 462}$

• Therefore remaining area is 462 cm²

@MissOxford