The curved surface area of a cone is $ 5544 \text{ cm}^2 $, an... | Mathematics MCQ | Examoogle

MathematicsPrevious Year Paper 2024

The curved surface area of a cone is $5544 \text{ cm}^2$ , and the diameter is $168 \text{ cm}$ . What is its total surface area (in $\text{cm}^2$ )? (Use $\pi = \frac{22}{7}$ )

27,270

27,720

25,530

23,550

Correct Answer

📐 MA • Math Direct FormulaMathematicsPrevious Year Paper 2024

Option B

27,720

Quick Summary:

Calculate radius $r = 84$ , then find slant height $l = CSA / (\pi r) = 5544 / (22/7 \times 84) = 21$ . Finally, $TSA = CSA + \pi r^2 = 5544 + 22/7 \times 84^2$ .

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📐MAMath SolutionDirect Formula

📋 Given

Curved Surface Area (CSA) = 5544 cm², Diameter d = 168 cm, π = 22/7

🔢 Formula Used

CSA=πrlCSA = \pi r lCSA=πrl and TSA=πr(r+l)TSA = \pi r(r + l)TSA=πr(r+l)

⚡ Exam Hall Shortcut / Speed Trick

Calculate radius $r = 84$ , then find slant height $l = CSA / (\pi r) = 5544 / (22/7 \times 84) = 21$ . Finally, $TSA = CSA + \pi r^2 = 5544 + 22/7 \times 84^2$ .

⚠️ Common Student Trap / Pitfall

Students often calculate only the Curved Surface Area instead of Total Surface Area (CSA + base area) or confuse radius with diameter.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Find radius and slant height

Given diameter $d = 168$ cm, radius $r = 168/2 = 84$ cm. From $CSA = \pi r l = 5544$ , substitute $r=84$ and $\pi=22/7$ to find $l$ .

l=5544×722×84=21 cml = \frac{5544 \times 7}{22 \times 84} = 21 \text{ cm}l=22×845544×7​=21 cm

Calculate Total Surface Area (TSA)

The formula for Total Surface Area is $TSA = CSA + \pi r^2$ .

TSA=5544+(227×84×84)TSA = 5544 + \left( \frac{22}{7} \times 84 \times 84 \right)TSA=5544+(722​×84×84)

Final computation

Calculate $\frac{22}{7} \times 84 \times 84 = 22 \times 12 \times 84 = 22176$ . Add this to the CSA.

TSA=5544+22176=27720 cm2TSA = 5544 + 22176 = 27720 \text{ cm}^2TSA=5544+22176=27720 cm2

✅

B is correct because the total surface area calculated as CSA + base area is 27,720 cm².

Core Concepts Used

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Mensuration Surface Area of Cone Geometry

💡 EXAM TIP

Always remember that Total Surface Area includes the base of the solid, whereas Curved Surface Area excludes it. Similar logic applies to cylinders ( $2\pi rh + \pi r^2$ for one base).

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