Question
A road which is 7m wide surrounds a circular park whose circumference is 352m. Find the area of the road.
✓
Answer
Width of the road = 7m
Circumference of the park = 352m Let r be the radius, then $2\pi\text{r}=352$ $\Rightarrow2\times\frac{22}{7}\text{r}=352\Rightarrow\text{r}=\frac{352\times7}{2\times22}$ ⇒ r = 56m Width of outer road = 7m $\therefore$ outer radius (R) = 56+7 = 63m $\therefore\text{Area of the road}=\pi\text{R}^2-\pi\text{r}^2$ $=\pi(\text{R}^2-\text{r}^2)=\frac{22}{7}(63^2-56^2)\text{m}^2$ $=\frac{22}{7}(63+56)(63-56)\text{m}^2$ $=\frac{22}{7}\times119\times7=2618\text{m}^2$
Circumference of the park = 352m Let r be the radius, then $2\pi\text{r}=352$ $\Rightarrow2\times\frac{22}{7}\text{r}=352\Rightarrow\text{r}=\frac{352\times7}{2\times22}$ ⇒ r = 56m Width of outer road = 7m $\therefore$ outer radius (R) = 56+7 = 63m $\therefore\text{Area of the road}=\pi\text{R}^2-\pi\text{r}^2$ $=\pi(\text{R}^2-\text{r}^2)=\frac{22}{7}(63^2-56^2)\text{m}^2$ $=\frac{22}{7}(63+56)(63-56)\text{m}^2$ $=\frac{22}{7}\times119\times7=2618\text{m}^2$
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