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What is the total surface area of a cylinder whose radius is 7 cm and height is 10 cm? (Use pi = 22/7)

$440 \text{ cm}^2$

$660 \text{ cm}^2$

$748 \text{ cm}^2$

$880 \text{ cm}^2$

Correct Answer

📐 MA • Math Direct FormulaMathematicsGeometry

Option C

$748 \text{ cm}^2$

Quick Summary:

Since the formula is $2 imes (22/7) imes 7 imes (7+10)$ , the $7$ cancels out. Mentally calculate $44 imes 17$ . Using distributive property: $44 imes 10 = 440$ and $44 imes 7 = 308$ . Sum is $748$ .

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📐MAMath SolutionDirect Formula

📋 Given

Radius r = 7 cm, height h = 10 cm, and pi = 22/7.

🔢 Formula Used

TSA=2πr(r+h)TSA = 2\pi r(r + h)TSA=2πr(r+h)

⚡ Exam Hall Shortcut / Speed Trick

Since the formula is $2 imes (22/7) imes 7 imes (7+10)$ , the $7$ cancels out. Mentally calculate $44 imes 17$ . Using distributive property: $44 imes 10 = 440$ and $44 imes 7 = 308$ . Sum is $748$ .

⚠️ Common Student Trap / Pitfall

Many students calculate only the lateral surface area ( $2 \pi rh = 440$ ) and mistakenly choose Option A instead of calculating the total surface area which includes the two circular bases.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify parameters

We are given the radius $r = 7$ cm and the height $h = 10$ cm of the cylinder.

r=7,h=10r = 7, h = 10r=7,h=10

Apply total surface area formula

The total surface area (TSA) of a cylinder is the sum of the lateral surface area and the areas of the two circular ends, given by the formula $TSA = 2\pi r(r + h)$ .

TSA=2imes227imes7imes(7+10)TSA = 2 imes \frac{22}{7} imes 7 imes (7 + 10)TSA=2imes722​imes7imes(7+10)

Simplify and Calculate

Cancel $7$ from the numerator and denominator, then multiply: $2 imes 22 imes 17$ . This results in $44 imes 17 = 748$ .

TSA=44imes17=748 cm2TSA = 44 imes 17 = 748 \text{ cm}^2TSA=44imes17=748 cm2

✅

C is correct because the calculated total surface area using the formula $2\pi r(r+h)$ yields exactly 748 cm².

Core Concepts Used

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Mensuration of 3D objects Cylinder properties Surface area calculation

💡 EXAM TIP

Always remember the difference between Lateral Surface Area ( $2\pi rh$ ) and Total Surface Area ( $2\pi rh + 2\pi r^2$ ). This distinction is frequently tested in exams like RRBJE, SSC, and UPSC CDS.

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