A circular field is surrounded by a path 2 m wide. If the inner radius is 10 m, find the cost to pave the path at ₹20 per m².
₹2765.71
Inner radius r = 10 m; the path is 2 m wide, so the outer radius R = 12 m.
Area of the path = \(\pi (R^2 - r^2) = \frac{22}{7}(144 - 100) = \frac{22}{7} \times 44 = \frac{968}{7} \approx 138.29\) m2.
Cost = \(\frac{968}{7} \times 20 = \frac{19360}{7} \approx 2765.71\).
Hence, the cost to pave the path is ₹2765.71.
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Important Questions from 2-D Mensuration
- The length of a rectangular plot is $(x^2 + xy + y^2)$ m and its breadth is $(x^2 - 5xy - y^2)$ m.
Find its perimeter, when $x = 1$ and $y = -1$. - The ratio between the perimeter and breadth of a rectangle is 3: 1. If the area of the rectangle is $98 \text{ cm}^2$, find the perimeter (in cm) of the rectangle.
The shorter side of a rectangle is 15 cm less than the longer side. The numerical value of its area is equal to 5 times the numerical value of its perimeter. What is the length (in cm) of its longer side?
- In a circle of radius 10.5 cm, if the angle of a sector is $\frac{2\pi}{3}$, then the perimeter of the sector is (in cm):
(Take $\pi = \frac{22}{7}$) - Find the circumference (in m) of the largest circle that can be inscribed in a rectangle whose dimensions are given as 114 m and 63 m.
Take $\pi = \frac{22}{7}$
