Question 12 Marks
Measure the circumference of any cylindrical object using a thread.
Answer
View full question & answer→SELF
Questions
2 Mark Question
Take a timed test
6 questions · self-marked practice — reveal the answer and mark yourself.
Question 22 Marks
Measure the circumference of a bangle with the help of a thread.
Answer
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Question 32 Marks
Place a cylindrical bottle on a paper and trace the outline of its base. Use a thread to measure the circumference of the circle.
Answer
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Question 42 Marks
Measure the circumference and diameter of the objects given below and enter the ratio of the circumference to its diameter in the table.
Examine the ratio of the circumference to the diameter. What do we see ?
Examine the ratio of the circumference to the diameter. What do we see ?
Answer
View full question & answer→The ratio of circumference to the diameter is same and is approximately equal to 3.14.
Question 52 Marks
Complete the table below :
| Sr. No | Radius (r) | Diameter (d) | Circumference (c) |
| i. | 7 cm | ||
| ii. | 28 cm | ||
| iii. | 616 cm | ||
| iv. | 72.6 cm |
Answer
View full question & answer→"i. Radius $(r)=7 cm$
Diameter $( d )=2 r$ $=2 \times 7=14 cm$
Circumference (c) $=\pi d$ $=\frac{22}{7} \times 14$
$=44 cm$ ii. Diameter $( d )=28 cm$
Radius $(r)=\frac{d}{2}=\frac{28}{2}=14 cm$
Circumference $(c)=\pi d$
$
\begin{aligned}
& =\frac{22}{7} \times 28 \\
& =88 cm
\end{aligned}
$ \begin{aligned}
& \text { iii. Circumference }( c )=616 cm \\
& \therefore \pi d =616 \\
& \therefore \frac{22}{7} \times d =616 \\
& \therefore d =616 \times \frac{7}{22} \\
& \therefore d =196 cm \\
& \therefore \text { Diameter (d) }=196 cm \\
& \text { Radius }( r )=\frac{ d }{2}=\frac{196}{2}=98 cm
\end{aligned} \begin{aligned}
& \text { iv. Circumference }( c )=72.6 cm \\
& \therefore \pi d =72.6 \\
& \frac{22}{7} \times d =72.6 \\
& \therefore d=72.6 \times \frac{7}{22}=\frac{726}{10} \times \frac{7}{22}=\frac{33 \times 7}{10} \\
& \therefore d =23.1 cm \\
& \therefore \text { Diameter }( d )=23.1 cm \\
& \text { Radius }( r )=\frac{ d }{2}=\frac{23.1}{2} \\
& =11.55 cm
\end{aligned}
Diameter $( d )=2 r$ $=2 \times 7=14 cm$
Circumference (c) $=\pi d$ $=\frac{22}{7} \times 14$
$=44 cm$ ii. Diameter $( d )=28 cm$
Radius $(r)=\frac{d}{2}=\frac{28}{2}=14 cm$
Circumference $(c)=\pi d$
$
\begin{aligned}
& =\frac{22}{7} \times 28 \\
& =88 cm
\end{aligned}
$ \begin{aligned}
& \text { iii. Circumference }( c )=616 cm \\
& \therefore \pi d =616 \\
& \therefore \frac{22}{7} \times d =616 \\
& \therefore d =616 \times \frac{7}{22} \\
& \therefore d =196 cm \\
& \therefore \text { Diameter (d) }=196 cm \\
& \text { Radius }( r )=\frac{ d }{2}=\frac{196}{2}=98 cm
\end{aligned} \begin{aligned}
& \text { iv. Circumference }( c )=72.6 cm \\
& \therefore \pi d =72.6 \\
& \frac{22}{7} \times d =72.6 \\
& \therefore d=72.6 \times \frac{7}{22}=\frac{726}{10} \times \frac{7}{22}=\frac{33 \times 7}{10} \\
& \therefore d =23.1 cm \\
& \therefore \text { Diameter }( d )=23.1 cm \\
& \text { Radius }( r )=\frac{ d }{2}=\frac{23.1}{2} \\
& =11.55 cm
\end{aligned}
| Sr. No | Radius (r) | Diameter (d) | Circumference (c) |
| i. | 7 cm | 14 cm | 44 cm |
| ii. | 14 cm | 28 cm | 88 cm |
| iii. | 98 cm | 196 cm | 616 cm |
| iv. | 11.55 cm | 23.1 cm | 72.6 cm |
Question 62 Marks
If the circumference of a circle is 176 cm, find its radius.
Answer
View full question & answer→Circumference $( c )=176 cm$
$
\begin{aligned}
& \therefore 2 \pi r =176 \\
& \therefore 2 \times \frac{22}{7} \times r =176 \\
& \therefore \frac{44}{7} xr =176 \\
& \therefore r =176 \times \frac{7}{44}=28 cm
\end{aligned}
$
$\therefore$ The radius of the circle is $28 cm$.
$
\begin{aligned}
& \therefore 2 \pi r =176 \\
& \therefore 2 \times \frac{22}{7} \times r =176 \\
& \therefore \frac{44}{7} xr =176 \\
& \therefore r =176 \times \frac{7}{44}=28 cm
\end{aligned}
$
$\therefore$ The radius of the circle is $28 cm$.