Question

a perfectly spherical orange is split into four equal sections. if the radius of the orange is 4 centimeters, what is the total surface area of one slice? 16π cm² 32π cm² 24π cm² 64π cm²

Explanation:

Step1: Find sphere surface area

The formula for the surface area of a sphere is $SA_{sphere}=4\pi r^2$. Substitute $r=4$ cm:
$$SA_{sphere}=4\pi (4)^2=64\pi \text{ cm}^2$$

Step2: Slice's curved surface share

Since the sphere is split into 4 equal slices, the curved surface area of one slice is $\frac{1}{4}$ of the total sphere surface area:
$$SA_{curved}=\frac{1}{4} \times 64\pi=16\pi \text{ cm}^2$$

Step3: Calculate area of two triangular faces

Each slice has two semicircular (now triangular) flat faces that form a full circle when combined. The area of a circle is $\pi r^2$:
$$SA_{flat}=\pi (4)^2=16\pi \text{ cm}^2$$

Step4: Sum all surface areas

Add the curved surface area and the flat surface areas of the slice:
$$SA_{total}=16\pi + 16\pi=32\pi \text{ cm}^2$$

Answer:

32π cm²