A hollow cylindrical pipe has an external radius of $ 7\text{ ... | Mathematics MCQ | Examoogle

MathematicsMensuration

A hollow cylindrical pipe has an external radius of $7\text{ cm}$ , internal radius of $6\text{ cm}$ , and height of $20\text{ cm}$ . Find the total surface area of the pipe (both ends included). $\left(\text{Use } \pi = \frac{22}{7}\right)$

1600 cm²

1716 cm²

1485 cm²

1670 cm²

Correct Answer

📐 MA • Math Direct FormulaMathematicsMensuration

Option B

1716 cm²

Quick Summary:

Calculate the surface area as: $2 \times \frac{22}{7} \times [R \times h + r \times h + (R^2 - r^2)]$ . Since $R^2 - r^2 = (7+6)(7-6) = 13$ , substitute values: $2 \times \frac{22}{7} \times [7(20) + 6(20) + 13] = 2 \times \frac{22}{7} \times 273 = 44 \times 39 = 1716$ .

🎯

Crack Mensuration with Examoogle SuperTeachers

Get Free Demo Classes & Live Mocks →

📐MAMath SolutionDirect Formula

📋 Given

External radius R = 7 cm, internal radius r = 6 cm, height h = 20 cm, and pi = 22/7.

🔢 Formula Used

TSA=2π(R+r)(h+R−r)+2π(R2−r2)TSA = 2\pi(R + r)(h + R - r) + 2\pi(R^2 - r^2)TSA=2π(R+r)(h+R−r)+2π(R2−r2)

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Students often calculate the Lateral Surface Area $(2\pi Rh + 2\pi rh)$ and forget to add the area of the two circular rings at the top and bottom $(2 \times \pi(R^2 - r^2))$ .

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate lateral surface areas

Calculate the sum of the external and internal curved surface areas using the formula $2\pi Rh + 2\pi rh$ .

2×227×(7×20+6×20)=2×227×260=1144072 \times \frac{22}{7} \times (7 \times 20 + 6 \times 20) = 2 \times \frac{22}{7} \times 260 = \frac{11440}{7}2×722​×(7×20+6×20)=2×722​×260=711440​

Calculate area of the two rings

Calculate the area of the two circular ring-shaped ends using $2 \times \pi(R^2 - r^2)$ .

2×227×(72−62)=2×227×(49−36)=2×227×13=57272 \times \frac{22}{7} \times (7^2 - 6^2) = 2 \times \frac{22}{7} \times (49 - 36) = 2 \times \frac{22}{7} \times 13 = \frac{572}{7}2×722​×(72−62)=2×722​×(49−36)=2×722​×13=7572​

Calculate total surface area

Add the lateral surface area and the area of the ends: $\frac{11440}{7} + \frac{572}{7} = \frac{12012}{7}$ .

120127=1716\frac{12012}{7} = 1716712012​=1716

✅

B is correct because the total surface area calculation results in exactly 1716 cm².

Core Concepts Used

Click any tag to open in AI Tutor

Cylinder Geometry Surface Area of Hollow Cylinder Area of Circular Ring

💡 EXAM TIP

This formula is a specific application of the general surface area of a composite solid; remember to always check if the ends are 'open' or 'closed' in such problems.

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)