Question

A circular park, 42 m in diameter, has a path 3.5 m wide running around it on the outside. find the cost of gravelling the path at rs. 4 per m2

Answer 1

✬ Total Cost = Rs 10010 ✬

Explanation:

Given:

• Diameter of circular park is 42 m.
• Length of path which is running around outside of this park is 3.5 m
• Cost of gravelling the path is Rs 4/m².

To Find:

• What is the total cost of gravelling ?

Solution: Diameter of circular park is 42 m therefore radius of circular park will be

➮ Radius = Diameter/2

➮ Radius = 42/2 = 21 cm

• Since, a path of 3.5 m is running around it on outside therefore:-

➮ Radius of outer circle = ( Radius of inner circle + 3.5 m )

➮ Radius of outer circle = (21+3.5) = 24.5 m.

★ Area of path = π [ (Radius of outer circle)² – (Radius of inner circle)² ] ★

$\implies$ π [ (24.5)² – (21)² ] m²

$\implies$ π [ (600.25 – 441) ] m²

$\implies$ π $\times$ 159.25 m²

$\implies$ 22/7 $\times$ 159.25 m²

$\implies$ 22 $\times$ 22.75 m²

$\implies$ 500.5 m²

So, the area of path is 500.5 m².

Now, Cost of gravelling 1 m² = Rs 4

∴ Cost of gravelling 500.5 m²

➨ Rs (500.5 $\times$ 4)

➨ Rs 10010

Answer 2

$\huge{\mathbb{\red{Answer}}}$

⭐Total Cost = Rs 10010 ⭐

$\huge{\mathbb{\red{Given}}}$

Diameter of circular park is 42 m.

Length of path which is running around outside of this park is 3.5 m

Cost of gravelling the path is Rs 4/m².

$\huge{\mathbb{\red{To find}}}$

What is the total cost of gravelling ?

$\huge{\mathbb{\red{solution}}}$

Diameter of circular park is 42 m therefore radius of circular park will be

➮ Radius = Diameter/2

➮ Radius = 42/2 = 21 cm

• Since, a path of 3.5 m is running around it on outside therefore:-

➮ Radius of outer circle = ( Radius of inner circle + 3.5 m )

➮ Radius of outer circle = (21+3.5) = 24.5 m.

★ Area of path = π [ (Radius of outer circle)² – (Radius of inner circle)² ] ★

\implies⟹ π [ (24.5)² – (21)² ] m²

\implies⟹ π [ (600.25 – 441) ] m²

\implies⟹ π \times× 159.25 m²

\implies⟹ 22/7 \times× 159.25 m²

\implies⟹ 22 \times× 22.75 m²

\implies⟹ 500.5 m²

So, the area of path is 500.5 m².

Now, Cost of gravelling 1 m² = Rs 4

∴ Cost of gravelling 500.5 m²

➨ Rs (500.5 \times× 4)

➨ Rs 10010

$\huge{\mathbb{\red{rupees.10010}}}$

$\huge{\mathfrak{\blue{Thanks}}}$