Question

question what is the volume of a hemisphere with a radius of 9.2 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 full - sphere is $V_{sphere}=\frac{4}{3}\pi r^{3}$. The volume of a hemisphere is half of the volume of a full - sphere, so $V_{hemisphere}=\frac{1}{2}\times\frac{4}{3}\pi r^{3}=\frac{2}{3}\pi r^{3}$.

Step2: Substitute the given radius

Given $r = 9.2$ cm. Substitute $r$ into the formula: $V=\frac{2}{3}\pi(9.2)^{3}$. First, calculate $(9.2)^{3}=9.2\times9.2\times9.2 = 778.688$. Then, $V=\frac{2}{3}\pi\times778.688$.

Step3: Calculate the value

$V=\frac{2\times778.688\pi}{3}=\frac{1557.376\pi}{3}\approx\frac{1557.376\times3.14159}{3}$. $1557.376\times3.14159 = 4899.477$. Then $V=\frac{4899.477}{3}=1633.159\approx1633.2$ $cm^{3}$.

Answer:

$1633.2$