Question

6 find the volume if the diameter of the fish tank is 30 cm using v = \frac{4}{3}\pi r^{3}: a 113,097 cm³ b 900 cm³ c 14,137 cm³ d 90,000 cm³

Explanation:

Step1: Find the radius

The radius $r$ is half of the diameter. Given $d = 30$ cm, so $r=\frac{d}{2}=\frac{30}{2}=15$ cm.

Step2: Substitute into volume formula

The volume formula is $V = \frac{4}{3}\pi r^{3}$. Substitute $r = 15$ cm into it: $V=\frac{4}{3}\pi(15)^{3}$.
First, calculate $(15)^{3}=15\times15\times15 = 3375$. Then $V=\frac{4}{3}\pi\times3375$.
$\frac{4}{3}\times3375 = 4500$. So $V = 4500\pi$.
Taking $\pi\approx3.14$, we have $V\approx4500\times3.14=14130$ $cm^{3}$, which is closest to $14137$ $cm^{3}$.

Answer:

C. $14,137$ $cm^{3}$