Find the total surface area of a cylinder whose radius is 7 cm... | Mathematics MCQ | Examoogle

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

$748 \text{ cm}^2$

$648 \text{ cm}^2$

$848 \text{ cm}^2$

$548 \text{ cm}^2$

Correct Answer

📐 MA • Math Direct FormulaMathematicsGeometry

Option A

$748 \text{ cm}^2$

Quick Summary:

Since the radius is 7, the area formula $2 imes (22/7) imes 7 imes (7 + 10)$ simplifies to $44 imes 17$ . Multiplying $44 imes 17$ is easy: $44 imes 10 = 440$ and $44 imes 7 = 308$ ; $440 + 308 = 748$ .

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📐MAMath SolutionDirect Formula

📋 Given

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

🔢 Formula Used

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

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Students often use the formula for Lateral Surface Area ( $2\pi rh$ ) instead of Total Surface Area ( $2\pi r(r+h)$ ), ignoring 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 formula for the total surface area of a cylinder is the sum of its lateral surface area and the areas of the two circular bases.

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

Substitute and Solve

Substituting $r = 7$ , $h = 10$ , and $\pi = 22/7$ : $TSA = 2 imes (22/7) imes 7 imes (7 + 10) = 44 imes 17$ .

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

✅

A is correct because the calculated total surface area is 748 cm².

Core Concepts Used

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Cylinder Geometry Surface Area calculation Mensuration

💡 EXAM TIP

This concept is foundational for understanding volume of composite solids where you may need to subtract shared surfaces (e.g., when a cylinder is joined to a hemisphere).

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