Question

select the correct answer from each drop-down menu. how can the surface area of the onion be approximated? image of onion with 3.5 in (width) and 3.6 in (height) the surface area of the onion can best be modeled by a sphere (drop - down). based on the model, the approximate surface area of the onion is drop - down with 58.8, 38.5, 74.2 square inches. buttons: reset, next.

Explanation:

Step1: Determine the radius of the sphere

The onion is modeled as a sphere. The diameter can be approximated by the average of the given dimensions (3.5 in and 3.6 in). First, find the average diameter: $\frac{3.5 + 3.6}{2} = 3.55$ in. Then the radius $r$ is half of the diameter: $r=\frac{3.55}{2}=1.775$ in (we can also use a more approximate value, or notice that maybe we can use an approximate diameter, but let's use the formula for surface area of a sphere: $SA = 4\pi r^{2}$). Alternatively, maybe the diameter is approximately 3.5 or 3.6, let's check with radius around 1.75 (since 3.5/2=1.75).

Step2: Calculate the surface area of the sphere

The formula for the surface area of a sphere is $SA = 4\pi r^{2}$. Let's use $r = 1.75$ (since 3.5 in is a diameter, so radius 1.75). Then $SA=4\times\pi\times(1.75)^{2}$. Calculate $(1.75)^{2}=3.0625$. Then $4\times\pi\times3.0625 = 12.25\pi\approx12.25\times3.14 = 38.465$, which is approximately 38.5. Wait, but let's check with the other dimension. If diameter is 3.6, radius is 1.8. Then $SA = 4\pi(1.8)^{2}=4\pi\times3.24 = 12.96\pi\approx40.7$, but the options are 58.8, 38.5, 74.2. Wait, maybe I made a mistake. Wait, maybe the onion is modeled as a sphere with diameter around 3.5 or 3.6, but let's recalculate. Wait, maybe the formula is $SA = 4\pi r^{2}$, and if we take the average diameter as (3.5 + 3.6)/2 = 3.55, radius 1.775. Then $SA = 4\times3.14\times(1.775)^{2}$. Calculate $(1.775)^2 = 3.150625$. Then $4\times3.14\times3.150625 = 12.56\times3.150625\approx39.5$, close to 38.5. Alternatively, maybe the problem uses a simplified $\pi\approx\frac{22}{7}$. Let's try that. If radius is 1.75 (diameter 3.5), then $SA = 4\times\frac{22}{7}\times(1.75)^{2}$. $(1.75)^2 = \frac{7}{4}\times\frac{7}{4}=\frac{49}{16}$. Then $4\times\frac{22}{7}\times\frac{49}{16}=\frac{4\times22\times49}{7\times16}=\frac{4\times22\times7}{16}=\frac{616}{16}=38.5$. Ah, that's it! So using $\pi=\frac{22}{7}$ and radius $r = \frac{3.5}{2}=1.75=\frac{7}{4}$ inches. Then the surface area is $4\times\frac{22}{7}\times(\frac{7}{4})^{2}=4\times\frac{22}{7}\times\frac{49}{16}=\frac{4\times22\times49}{7\times16}=\frac{4\times22\times7}{16}=\frac{616}{16}=38.5$ square inches.

Answer:

38.5