Answer:
134 cubic centimeters
Step-by-step explanation:
The extended part is basically the volume of HALF A SPHERE.
First, the volume of full sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Hence, the half sphere volume would be:
[tex]Half \ Sphere = \frac{\frac{4}{3}\pi r^3}{2}=\frac{2}{3}\pi r^3[/tex]
We know the diameter is 8, radius is HALF OF THAT, so
Radius = 8/2 = 4
Substituting, we find (remembering to use 3.14 as pi):
[tex]\frac{2}{3}\pi r^3\\=\frac{2}{3}\pi (4)^3\\=\frac{2}{3}(3.14)(64)\\=133.97[/tex]
To the nearest cubic centimeter, the answer is:
134 cubic centimeters
The volume of ice that extends above the cup to the nearest cubic centimeter is 134 cubic cm.
If the given sphere is of radius r units, then its half volume (or the volume of the hemisphere) is given as:
[tex]V= \dfrac{2}{3} \pi r^3 \: \rm unit^3[/tex]
For this case, we're specified that:
Radius of the sphere from which hemisphere's volume is to be known = 8 cm
Thus, we get:
[tex]\text{Volume of hemisphere} = V = \dfrac{2}{3} \pi r^3 \: \rm unit^3\\\\V = \dfrac{2}{3} \pi r^3 \approx \dfrac{2}{3} \times 3.14 \times (4)^3 \approx 134\: \rm cm^3[/tex]
Thus, the volume of ice that extends above the cup to the nearest cubic centimeter is 134 cubic cm.
Learn more about volume of hemisphere here:
https://brainly.com/question/13250046
