Question

Calculate the area and perimeter of the following ring where a = 7cm, b = 14cm

Answer 1

Given : a ring inner radius = 7 cm & outer radius = 14 cm

To find : Area of Ring and Perimeter of Ring: 132 cm

Solution:

Area of circle = π Radius²

Perimeter of circle = 2π Radius

Area of ring

= Area of bigger circle - area of smaller circle

= π (14)² - π (7)²

= π(14 + 7)(14 - 7)

= π(21)(7)

use π = 22/7

= (22/7)(21)(7)

= 462 cm²

Perimeter of ring

Area of bigger circle + area of smaller circle

= 2π(14) + 2π(7)

= 2π(21)

= 2(22/7)(21)

= 132 cm

Area of Ring: 462 cm²

Perimeter of Ring: 132 cm

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Answer 2

Given:

$a = 7\ cm\\b = 14\ cm$

To find:

area of circle=?

The perimeter of circle=?

Solution:

Formula:

$\ Area \ of \ circle \ = \pi \times \ r^2\\\ The \ Perimeter \ of \ circle\ = \ 2 \times \pi \times r$

Finding the area of the circle:

To calculate the ring area we subtract a big circle to the small circle:

$\to \pi r^2-\pi r^2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ _{where}(\pi = \frac{22}{7})\\\\ \to \frac{22}{7} \times (14)^2-\frac{22}{7} \times (7)^2\\\\\ \to \frac{22}{7} \times 14\times 14-\frac{22}{7} \times 7\times7\\\\\ \to 22 \times 2\times 14- 22 \times7\\\\\ \to 44\times 14- 22 \times7\\\\\ \to 616- 154\\\\\to 462\ cm^2$

To calculate perimeter we add both perimeter value:

$\to 2\times \pi\times r+2\times \pi\times r\\\\\to 2\times \frac{22}{7}\times 14+ 2\times \frac{22}{7}\times 7\\\\\to 2\times 22\times 2+ 2\times 22\times 1\\\\\to 88+ 44\\\\\to 132 \ cm$

The final answer is 462 and 132 .