An open cone with base radius 28cm and perpendicular height 96cm was stretched to form...

WAEC 2013

An open cone with base radius 28cm and perpendicular height 96cm was stretched to form sector of a circle. calculate the arc of the sector (Take \(\pi = \frac{22}{7}\))

A. 8800cm²
B. 8448cm²
C. 4400cm²
D. 4224cm²

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Correct Answer: Option A

Explanation

L² = 96² + 28²

= 9216 + 784

= 10000

L = \(\sqrt{10000}\)

= 100cm

curved surface area = \(\pi r l\)

= \(\frac{22}{7} \times 28 \times 100\)

= 8800cm²

area of cone = area of sector

area of sector = 8800cm²

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