Question

What is the volume of a hemisphere with a diameter of 8.9 cm, rounded to the nearest tenth of a cubic centimeter?

Answer 1

The volume of a hemisphere with a diameter of 8.9 cm is approximately 373.9 cm³.

Step-by-step explanation:

The volume of a hemisphere can be calculated using the formula for the volume of a sphere, which is V = (4/3)π r3. However, since we are dealing with a hemisphere, we need to divide the result by 2 to get half the volume of a sphere. The diameter of the hemisphere is given as 8.9 cm, so the radius is half of that, which is 4.45 cm.

Using the formula and substituting the value of the radius, we can calculate the volume as follows:

V = (4/3)π(4.45 cm)3

V = (4/3)π(89.3025 cm3)

V = (4/3)(3.14)(89.3025 cm3)

V = 373.919 cm3

Since the question asks us to round to the nearest tenth of a cubic centimeter, the final answer is 373.9 cm3.

Answer 2

We're going through all the shapes.

A sphere has volume

`V_{\textrm{sphere}}= \frac 4 3 \pi r^3`

A hemisphere has half the volume and a radius is half a diameter.

`V= \frac 1 2 (\frac 4 3) \pi (\frac d 2)^3 = (1)/(12) \pi d^3`

`V = (\pi)/(12) (8.9)^3 \approx 184.6 \textrm{ cc}`