Question

a hollow hemisphere is half of a sphere with a hollow center. there are two radii in a hollow hemisphere, the inner radius and the outer radius, as shown to the nearest 0.1 cubic centimeter, what is the volume of a hollow hemisphere with an inner radius of 1 centimeter and an outer radius of 3 centimeters?
a 56.5 cm³
b 54.5 cm³
c 30.6 cm³
d 16.8 cm³

Explanation:

Step1: Recall volume of hemisphere formula

The volume of a hemisphere is $\frac{2}{3}\pi r^3$. For a hollow hemisphere, we subtract the volume of the inner hemisphere from the outer hemisphere. So the formula is $V=\frac{2}{3}\pi (R^3 - r^3)$, where $R$ is outer radius and $r$ is inner radius.

Step2: Substitute values

Given $R = 3$ cm and $r = 1$ cm. Substitute into the formula: $V=\frac{2}{3}\pi(3^3 - 1^3)=\frac{2}{3}\pi(27 - 1)=\frac{2}{3}\pi\times26$.

Step3: Calculate the value

First, $\frac{2}{3}\times26=\frac{52}{3}$. Then multiply by $\pi$: $\frac{52}{3}\pi\approx\frac{52}{3}\times3.1416\approx54.5$ (rounded to nearest 0.1).

Answer:

B. $54.5\ \text{cm}^3$