A cylindrical tank has a radius of 7 m and a height of 10 m. I... | Mathematics MCQ | Examoogle

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A cylindrical tank has a radius of 7 m and a height of 10 m. If the cost of painting its lateral surface area is ₹ 20 per $\text{m}^2$ , find the total cost of painting. (Use $\pi = \frac{22}{7}$ )

8800

4400

6600

2200

Correct Answer

📐 MA • Math Direct FormulaMathematicsMensuration

Option A

8800

Quick Summary:

Note that the lateral surface area involves $2 \times \pi \times r$ . Since $\pi = 22/7$ and $r = 7$ , they cancel out: $2 \times 22 \times 10 = 440$ . Then $440 \times 20 = 8800$ .

📐MAMath SolutionDirect Formula

📋 Given

Radius of the cylinder r = 7 m, Height h = 10 m, Rate of painting = 20 per square meter.

🔢 Formula Used

Lateral Surface Area=2πrh,Total Cost=Area×Rate\text{Lateral Surface Area} = 2 \pi rh, \quad \text{Total Cost} = \text{Area} \times \text{Rate}Lateral Surface Area=2πrh,Total Cost=Area×Rate

⚡ Exam Hall Shortcut / Speed Trick

Note that the lateral surface area involves $2 \times \pi \times r$ . Since $\pi = 22/7$ and $r = 7$ , they cancel out: $2 \times 22 \times 10 = 440$ . Then $440 \times 20 = 8800$ .

⚠️ Common Student Trap / Pitfall

Students often calculate the Total Surface Area (including bases) instead of the Lateral Surface Area, which would lead to an incorrect answer.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate Lateral Surface Area

Use the formula for the lateral surface area of a cylinder: $2 \pi rh$ . Substituting $r = 7$ and $h = 10$ with $\pi = 22/7$ .

LSA=2×227×7×10=440 m2\text{LSA} = 2 \times \frac{22}{7} \times 7 \times 10 = 440 \text{ m}^2LSA=2×722​×7×10=440 m2

Calculate Total Cost

Multiply the calculated surface area by the given cost rate of 20 per square meter.

Total Cost=440×20=8800\text{Total Cost} = 440 \times 20 = 8800Total Cost=440×20=8800

✅

A is correct because the lateral surface area is 440 square meters, and at a rate of 20 per square meter, the total cost is 8800.

Core Concepts Used

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Cylinder Geometry Lateral Surface Area Cost Calculation

💡 EXAM TIP

This concept of lateral surface area is fundamental for calculating costs in painting or sheet-metal problems in competitive exams, often appearing alongside volume problems.

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