Jenny's birthday cake is circular and has a 30 cm radius. Her slice creates an arc with a central angle of 120 degrees. What is the area of Jenny's slice of cake? Give your answer in terms of [tex]\pi[/tex].
Answer (3)
Ok, so if the angle is 120 degrees, its one third of the full cake (which is 360 degrees). So the area of the whole circle (worked out with area = pi * r^2 where r is 30) gives 900*pi, and so one third of that (because her slice is one third) is 300pi.
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 π is 300 π
Given that
r = 30 c m --- the radius
θ = 12 0 o --- central angle
The **area of the slice **is calculated using the area of a sector , as follows:
A re a = 360 θ × π r 2
So, we have:
A re a = 360 120 × π × 3 0 2
A re a = 3 1 × π × 900
A re a = π × 300
A re a = 300 π
Hence, the **area **of the **slice of cake **is 300 π
Learn more about area of sectors at:
https://brainly.com/question/7512468
The area of Jenny's slice of cake is 300 π cm 2 . This is calculated using the sector area formula with a radius of 30 cm and a central angle of 120 degrees. The calculation shows that the slice takes up one-third of the circular cake's area.
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