Question

question what is the volume of a hemisphere with a radius of 3 cm, rounded to the nearest tenth of a cubic centimeter? answer attempt 1 out of 2 cm³ submit answer

Explanation:

Step1: Recall volume formula for sphere

The volume formula for a sphere is $V_{sphere}=\frac{4}{3}\pi r^{3}$. A hemisphere is half - of a sphere, so the volume formula for a hemisphere is $V_{hemisphere}=\frac{2}{3}\pi r^{3}$.

Step2: Substitute the radius value

Given $r = 3$ cm, substitute $r$ into the formula: $V=\frac{2}{3}\pi(3)^{3}$.
First, calculate $(3)^{3}=3\times3\times3 = 27$. Then, $V=\frac{2}{3}\pi\times27$.
$\frac{2}{3}\times27 = 18$, so $V = 18\pi$.

Step3: Calculate the numerical value and round

Using $\pi\approx3.14159$, $V=18\times3.14159 = 56.54862$.
Rounding to the nearest tenth, $V\approx56.5$ $cm^{3}$.

Answer:

$56.5$