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 $\therefore\text{Area of the road}=\pi\text{R}^2-\pi\text{r}^2$ $=\pi(\text{R}^2-\text{r}^2)=\frac{22}{7}(63^2-56^2)\text{m}^2$ $=\frac{22}{7}(63+56)(63-56)\text{m}^2$ $=\frac{22}{7}\times119\times7=2618\text{m}^2$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A circular park is surrounded by a rod $21\ m$ wide. If the radius of the park is $105\ m$, find the area of the road.
→Solve the following quadratic equations by factorization:
$\frac{\text{x}-3}{\text{x}+3}-\frac{\text{x}+3}{\text{x}-3}=\frac{48}{7},$ $\text{x}\neq3,\text{x}\neq-3$
→$\frac{\text{x}-3}{\text{x}+3}-\frac{\text{x}+3}{\text{x}-3}=\frac{48}{7},$ $\text{x}\neq3,\text{x}\neq-3$
A die is rolled twice. Find the probability that:5 will come up exactly one time.
Two dice are rolled together. Find the probability of getting such numbers on two dice whose product is a perfect square.
Short-Answer Question:
If $\alpha$ and $\beta$ are the zeroes of a polynomial $f(x) = 6x^2 + x - 2$, find the value of $\Big(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\Big).$
→If $\alpha$ and $\beta$ are the zeroes of a polynomial $f(x) = 6x^2 + x - 2$, find the value of $\Big(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\Big).$
Fill in the blanks given in the contract note of sale-purchase of shares.
(B - buy S - sell)
(B - buy S - sell)
A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck.
Using an appropriate method, find the mean of following frequency distribution:
Which method did you use, and why?
|
Class interval
|
84-90
|
90-96
|
96-102
|
102-108
|
108-114
|
114-120
|
|
Frequency
|
8
|
10
|
16
|
23
|
12
|
11
|
Evaluate the following:
If A = 60° and B = 30°, verify that:
$\sin(\text{A}-\text{B})=\sin\text{A}\cos\text{B}-\cos\text{A}\sin\text{B}$
→If A = 60° and B = 30°, verify that:
$\sin(\text{A}-\text{B})=\sin\text{A}\cos\text{B}-\cos\text{A}\sin\text{B}$
A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of the cone are 6cm and 4cm, respectively. Determine the surface area of the toy. $(\text{use}\ \pi=3.14)$
→