Question

Calculate
13. The area of a circular ring is 942.6 sq cm and the radius of the larger circle is 20 cm.
(a) the area of the smaller circle, and
(b) the uniform width of the ring. (Use a = 3.142)

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Answer 1

Answer:

• Thickness of the ring = 10 cm
• Area of smaller circle = 314.2 cm²

Given that,

Area of the ring = 942.6 cm²

Radius of the larger circle = 20 cm

To find,

Area of Smaller Circle = ?

The thickness of the ring = ?

Steps:

According to the diagram, the Area of the ring is nothing but the shaded portion of the ring. This is calculated by the formula:

→ Area of ring = Area of larger circle - Area of smaller circle

→ Area of smaller circle = Area of larger circle - Area of ring

Substituting the values, we get:

→ 942.6 cm² = πR² - πr²

→ πr² = (3.14 × 20 × 20) - 942.6 cm² -

→ πr² = 1256.8 cm² - 942.6 cm²

→ πr² = 314.2 cm²

Hence the area of the smaller circle is 314.2 cm².

→ Thickness of the ring = Radius of larger circle - Radius of the smaller circle

→ Thickness of the ring = 20 cm - r

From Area of smaller circle, we get the radius of the smaller circle to be:

→ πr² = 314.2 cm²

→ r² = (314.2 / π) = (314.2/3.142) = 100

⇒ r = √100 = 10 cm

Therefore the thickness of the ring can be calculated as:

→ Thickness of the ring = 20 cm - 10 cm = 10 cm

Hence thickness of the ring is 10 cm.

Answer 2

$\huge \fbox {Solution}$

Area of smaller circle = Area of larger circle - Area of ring

942.6 cm² = πR² - πr²

πr² = (3.14 × 20 × 20) - 942.6 cm²

πr² = (3.14 × 400) - 942.6 cm²

πr² = 1256.8 cm² - 942.6 cm²

πr² = 314.2 cm²

Now,

Thickness of ring = Radius of Bigger circle - Radius of smaller circle

πr² = 314.2 cm²

r² = (314.2 / π) = (314.2/3.142)

r² = 100

r = √100 = 10 cm