Explanation

(a) Length of the arc XY = Circumference of the base.

\(\frac{\theta}{360°} \times 2\pi r\)

where \(\theta\) = 270° ; r = 7cm.

Length of arc XY = \(\frac{270°}{360°} \times 2 \times \frac{22}{7} \times 7 = 33cm\)

Let the radius of the base of the cone = x

\(2 \pi r = 33cm\)

\(2 \times \frac{22}{7} \times x = 33\)

\(\frac{44}{7} \times x = 33 \implies x = \frac{33 \times 7}{44}\)

\(x = 5.25cm\)

(b) Area of the base of the cone = \(\pi r^{2}\)

= \(\frac{22}{7} \times \frac{21}{4} \times \frac{21}{4}\)

= \(\frac{693}{8} cm^{2} = 86.625 cm^{2}\)

\(\approxeq 87 cm^{2}\)

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