The area of an ellipse is 132cm$^2$.The length of its major axis is 14cm.Find the length of its minor axis

1. Analyze the question

We are given the area of an ellipse ($132 \text{ cm}^2$) and the length of its major axis ($14 \text{ cm}$). We need to find the length of the minor axis.

2. Explain the concept

• The formula for the area of an ellipse is: Area = $\pi ab$ • Where $a$ is the semi-major axis (half of the major axis). • Where $b$ is the semi-minor axis (half of the minor axis).
• The length of the major axis is $2a$, and the length of the minor axis is $2b$.
• We will use $\pi \approx \frac{22}{7}$ as is standard for JAMB questions involving multiples of 7 or 11.

3. Show the solution

Step 1: Find the semi-major axis ($a$). The major axis is $14 \text{ cm}$. $2a = 14$ $a = \frac{14}{2} = 7 \text{ cm}$

Step 2: Use the area formula to find the semi-minor axis ($b$). Area = $\pi ab$ $132 = \frac{22}{7} \times 7 \times b$

The $7$ in the numerator and denominator cancel out: $132 = 22 \times b$ $b = \frac{132}{22}$ $b = 6 \text{ cm}$

Step 3: Find the length of the minor axis ($2b$). Minor axis = $2 \times b$ Minor axis = $2 \times 6 = 12 \text{ cm}$

4. Identify the answer

Comparing our result ($12 \text{ cm}$) to the given options, the correct choice is D.

5. Tip

When dealing with circles or ellipses in JAMB, always check if the area or radius involves multiples of 7 or 11. If it does, using $\pi = \frac{22}{7}$ will make your calculation much faster and cleaner than using $3.142$.