Question : The diameter of a circle is $\frac{7}{4}$ times the base of a triangle, and the height of the triangle is 14 cm. If the area of the triangle is 56 cm2, then what is the circumference (in m) of the circle? (Use $\pi=\frac{22}{7}$)
Option 1: 0.44 m
Option 2: 2.46 m
Option 3: 0.48 m
Option 4: 1.74 m
Correct Answer: 0.44 m
Solution :
Given: The diameter of a circle is $\frac{7}{4}$ times the base of a triangle, and the height of the triangle is 14 cm.
The area of the triangle is 56 cm
2
.
Use the formulas,
The diameter of the circle = $2r$,
The circumference of the circle = $2\pi r$,
The area of the triangle = $\frac{1}{2}\times \text{base}\times \text{height}$
where $r$ is the radius of the circle.
According to the question,
$\frac{1}{2}\times \text{base}\times {14}=56$
⇒ $\text{base}=8$ cm
The diameter of a circle $=\frac{7}{4}\times 8=14$ cm.
The radius of a circle $= \frac{14}{2}=7$ cm.
The circumference of the circle $= 2\times \frac{22}{7}\times 7 = 44$ cm
Now, 44 cm = $\frac{44}{100}$ m = 0.44 m
Hence, the correct answer is 0.44 m.
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