If the lateral surface area of a cylinder is 775.8 cm 2 and it... | Mathematics MCQ | Examoogle

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If the lateral surface area of a cylinder is 775.8 cm 2 and its height is 24 cm, then find its volume. (Use π = 3.14 and round off to two decimal places.)

1962.74 cm³

1984.78 cm³

2016.67 cm³

1996.63 cm³

Correct Answer

📐 MA • Math Direct FormulaMathematicsMensuration

Option D

1996.63 cm³

Quick Summary:

Calculate the radius first using $r = \frac{LSA}{2 \pi h}$ . Given $2 \pi h \approx 2 \times 3.14 \times 24 = 150.72$ , dividing $775.8$ by $150.72$ gives $r \approx 5.147$ . Then estimate volume $V = \pi r^2 h = (\frac{LSA}{2}) \times r$ .

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📐MAMath SolutionDirect Formula

📋 Given

Lateral surface area of cylinder LSA = 775.8 cm², height h = 24 cm, and $\pi$ = 3.14.

🔢 Formula Used

LSA=2πrhLSA = 2 \pi r hLSA=2πrh and V=πr2hV = \pi r^2 hV=πr2h

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Students often use the diameter instead of the radius in the volume formula or use the total surface area formula instead of lateral surface area.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate the radius of the cylinder

Using the formula for lateral surface area $LSA = 2 \pi r h$ , substitute the known values to find $r$ .

r=775.82×3.14×24=775.8150.72≈5.1473r = \frac{775.8}{2 \times 3.14 \times 24} = \frac{775.8}{150.72} \approx 5.1473r=2×3.14×24775.8​=150.72775.8​≈5.1473

Calculate the volume of the cylinder

Substitute the value of $r$ into the volume formula $V = \pi r^2 h$ .

V=3.14×(5.1473)2×24V = 3.14 \times (5.1473)^2 \times 24V=3.14×(5.1473)2×24

Perform final multiplication

Calculate the square of the radius and multiply by $\pi$ and $h$ to get the final volume.

V=3.14×26.4947×24≈1996.63V = 3.14 \times 26.4947 \times 24 \approx 1996.63V=3.14×26.4947×24≈1996.63

✅

D is correct because the calculated volume of the cylinder using the derived radius is approximately 1996.63 cm³.

Core Concepts Used

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Lateral Surface Area Volume of a Cylinder Geometry

💡 EXAM TIP

This concept is essential for mensuration problems in SSC and banking exams where cylindrical pipes or tank capacities are frequently asked.

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