Lesson Example Discussion Quiz: Class Homework |
Step-3 |
Title: Circles |
Grade: 8-a Lesson: S4-L2 |
Explanation: Let us verify the answer here with the steps. |
Description:
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
The sum of circumference and diameter of a circle is 203 cm, find the diameter of the circle. |
|
2 |
Hint |
Formula used |
\$"Area" = \pi \times r^2\$ |
3 |
Step |
Let the radius of the circle be 'r' cm |
|
4 |
Step |
Given that, The sum of circumference and diameter of a circle |
203 cm |
5 |
Step |
We know that the circumference of a circle with radius 'r’cm is given by \$2\pi r\$ and diameter of the circle is twice that of its radius. |
|
6 |
Step |
So, we have |
\$2\pi r + 2r = 203\$ ⇒ \$2\$ x \$22/7\$ x \$r\$ + \$2r\$ = 203 ⇒ r \$(44/7 + 2)\$ = 203 ⇒ r \$("44+14"/7)\$ = 203 ⇒ r \$("58"/7)\$ = 203 ⇒ r = 203 x \$("7"/58)\$ ⇒ r = \$24.5\$ cm |
7 |
Step |
As diameter is twice that of the radius, length of the diameter |
\$2\$ x \$24.5\$ ⇒ \$49\$ cm |
8 |
Step |
Thus, the length of the diameter |
\$49\$ cm |
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