Question

A ring-shaped disc has outer radius 10 cm and inner radius 7 cm. What is the approximate ratio of the ring's area to the whole outer circle?

• A. 1 : 2
• B. 2 : 3
• C. 3 : 4
• D. 4 : 5

Answer 1

Answer:

A. 1 : 2

Using $( \pi = \frac{22}{7} )$:

Ring area

$\text{Ring area} = \pi(10^2 - 7^2) = \frac{22}{7}(100 - 49) = \frac{22}{7} \times 51$

Outer circle area

$\text{Outer area} = \pi \times 10^2 = \frac{22}{7} \times 100$

Ratio

$\frac{\text{Ring area}}{\text{Outer area}} = \frac{\frac{22}{7} \times 51}{\frac{22}{7} \times 100} = \frac{51}{100}$

Approximation:

$\frac{51}{100} = 0.51 \approx 0.5 = \frac{1}{2}$

Final Answer:

$\boxed{1 : 2 \ (\text{approx})}$