When a circle (i.e. the cake) is cut through the radius, the parts formed are referred to as the sectors of the circle. The area of the slice in terms of[tex]\pi[/tex] is [tex]300 \pi[/tex]
Given that
[tex]r = 30cm[/tex] --- the radius
[tex]\theta = 120^o[/tex] --- central angle
The area of the slice is calculated using the area of a sector, as follows:
[tex]Area = \frac{\theta}{360} \times \pi r^2[/tex]
So, we have:
[tex]Area = \frac{120}{360} \times \pi \times 30^2[/tex]
[tex]Area = \frac{1}{3} \times \pi \times 900[/tex]
[tex]Area = \pi \times 300[/tex]
[tex]Area = 300\pi[/tex]
Hence, the area of the slice of cake is [tex]300\pi[/tex]
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