Question

tyler is building a fish tank in the shape of a sphere that has a diameter of 18 inches. based on tylers research, it is recommended to have no more than 1 goldfish for every 693 cubic inches of water. how many goldfish should tyler buy for his fish tank? numerical answers expected answer for blank 1:

Explanation:

Step1: Calculate volume of sphere

The volume formula for a sphere is $V = \frac{4}{3}\pi r^{3}$, where the radius $r=\frac{d}{2}$ and $d = 18$ inches, so $r = 9$ inches. Then $V=\frac{4}{3}\pi(9)^{3}=\frac{4}{3}\pi\times729 = 972\pi$ cubic - inches. Using $\pi\approx3.14$, we have $V\approx972\times3.14 = 3052.08$ cubic - inches.

Step2: Determine number of goldfish

We know that we should have no more than 1 goldfish for every 693 cubic - inches of water. Let $n$ be the number of goldfish. Then $n=\frac{V}{693}$. Substituting $V\approx3052.08$ into the formula, we get $n=\frac{3052.08}{693}\approx4.4$. Since we can't have a fraction of a goldfish and we must follow the "no more than 1 goldfish per 693 cubic - inches" rule, the number of goldfish is 4.

Answer:

4