Question

A conical container has a radius of 10 cm and a volume of 60π cm^3 . If the container is 3/4 filled with water, how many centimeters deep does the water fill the container?

A) 1.35 cm
B) 1.45 cm
C) 1.5 cm
D) 1.8 cm

Answer 1

Answer: A) 1.35 cm.

Explanation:
The volume VV of a cone is given by:

V=13πr2hV=31​πr2h

Where:

rr is the radius of the cone.

hh is the height of the cone.

Given:

r=10 cmr=10 cm

V=60π cm3V=60π cm3

Plugging in the given values:

60π=13π(102)h60π=31​π(102)h

From this equation, we can solve for hh, the height of the entire cone.

Once we have the height of the entire cone, we can determine the height of the water when the container is 3443​ filled.

Let's calculate the height hh of the cone first.

The height hh of the entire cone is 9559​ cm, which is equivalent to 1.8 cm.

Now, if the container is 3443​ filled with water, the height of the water hwaterhwater​ is:

hwater=34×1.8 cmhwater​=43​×1.8 cm

Let's calculate hwaterhwater​.

The height of the water when the container is 3443​ filled is 1.351.35 cm.