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1 month ago

CALC 1: Spud's mom is going to make him a round birthday cake, and has asked for your help. Spud is a bit weird, and has already

Mathematics

1 answer:

Svet_ta [12.7K]1 month ago

6 0

Answer:

15.7 inches

Step-by-step breakdown:

A slice of a round pie is a sector of a circle.

The perimeter of a slice equals the arc length s plus two times the radius r. P = s + 2r

s = rθ = r(16/360) = r/22.5. Therefore,

16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5

16 × 22.5 = 46r

360 = 46r

r = 7.826

D = 2r = 2 × 7.826 = 15.7 inches

Thus, the diameter of the cake should be 15.7 inches.

Verification:

$\begin{array}{rcl}P & = & s + 2r\\& = & \dfrac{r}{22.5} + 2r\\\\16 & = & \dfrac{7.826}{22.5} + 2 \times 7.826\\\\16 & = & 0.35 + 15.65\\16 & = & 16.00\\\end{array}$

It is accurate.

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