Find the perimeter of the semi-circle of radius 21 cm. (Take $... | Mathematics MCQ | Examoogle

Examoogle • User • info@examoogle.com • EE-2024-8821

Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked

Back to Practice Questions

MathematicsMensuration

Prev Next

Find the perimeter of the semi-circle of radius 21 cm. (Take $\pi = \frac{22}{7}$ ).

108 cm

174 cm

87 cm

66 cm

Correct Answer

📐 MA • Math Direct FormulaMathematicsMensuration

Option A

108 cm

Quick Summary:

For a semi-circle, the perimeter is always equal to $36/7$ of the radius when using $\pi = 22/7$ . Thus, calculate $\frac{36}{7} \times 21 = 36 \times 3 = 108$ .

🎯

Crack Mensuration with Examoogle SuperTeachers

Get Free Demo Classes & Live Mocks →

📐MAMath SolutionDirect Formula

📋 Given

Radius of the semi-circle r = 21 cm, value of pi is given as 22/7.

🔢 Formula Used

P=(π+2)×rP = (\pi + 2) \times rP=(π+2)×r

⚡ Exam Hall Shortcut / Speed Trick

For a semi-circle, the perimeter is always equal to $36/7$ of the radius when using $\pi = 22/7$ . Thus, calculate $\frac{36}{7} \times 21 = 36 \times 3 = 108$ .

⚠️ Common Student Trap / Pitfall

Students often calculate only the curved part ( $\pi r$ ) and forget to add the diameter ( $2r$ ) to close the semi-circle.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify the components of the perimeter

The perimeter of a semi-circle includes the length of the arc (which is half the circumference of a circle, i.e., $\pi r$ ) plus the length of the straight diameter ( $2r$ ).

P=πr+2r=r(π+2)P = \pi r + 2r = r(\pi + 2)P=πr+2r=r(π+2)

Substitute the given values

Given $r = 21$ cm and $\pi = 22/7$ , substitute these into the formula.

P=21×(227+2)P = 21 \times (\frac{22}{7} + 2)P=21×(722​+2)

Calculate the final result

Calculate the value inside the parentheses: $\frac{22}{7} + \frac{14}{7} = \frac{36}{7}$ . Then multiply by the radius.

P=21×367=3×36=108 cmP = 21 \times \frac{36}{7} = 3 \times 36 = 108 \text{ cm}P=21×736​=3×36=108 cm

✅

A is correct because the perimeter of a semi-circle with radius $21$ cm is calculated as $21 \times (\frac{22}{7} + 2) = 108$ cm.

Core Concepts Used

Click any tag to open in AI Tutor

Geometry Circle properties Mensuration

💡 EXAM TIP

This formulaic approach is similar to finding the perimeter of a sector, where $P = 2r + l$ and arc length $l = r\theta$ (in radians).

Was this solution helpful?

⚡ Practice on Android App · 4.8 ★

Solve 10,000+ More Questions with AI Tutor

Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.

Free Download • 100K+ Aspirants

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)