Nevernevergiveup wrote:

Attachment:

cup.png

A glass is shaped like a right circular cylinder with a half sphere at the bottom. The glass is 7cm deep and has a diameter of 6cm, measured on the inside. If the glass is filled to the rim with apple cider, how much cider is in the glass? The formula for the volume a sphere is \(\frac{4}{3}*\pi*r^3\).

A. 18\(\pi\)

B. 36\(\pi\)

C. 54\(\pi\)

D. 81\(\pi\)

E. 108\(\pi\)

The glass volume is composed of 2 parts: hemispherical portion + cylindrical portion.

For the hemispherical portion, diameter = 6 cm ---> radius = r= 3 ---> volume of the hemisphere = volume of sphere /2 = \(0.5*\frac{4}{3}*\pi*r^3 = 18\pi\)

For the cylindrical part, heigh=h=7-3 = 4 and radius =3 ---> volume of the cylindrical portion \(= \pi*r^2*h = 36\pi\)

Thus the total volume =\(( 18+36 )\pi = 54\pi\)

C is thus the correct answer.

Hope this helps.