SOLUTION: A paper cup is in the shape of a right circular cone with a diameter of 8cm and a height of 12cm. a.) Suppose the cup is filled with water to a depth of 8cm. Calculate the volum

Question 1143219: A paper cup is in the shape of a right circular cone with a diameter of 8cm and a height of 12cm.
a.) Suppose the cup is filled with water to a depth of 8cm. Calculate the volume of water in the cup. Round to the nearest whole number. (HINT: Use similar triangles.)
b.) To what depth must the cup be filled in order to be half full of water? Round to the nearest tenth.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The volume of the cup is

a. If the cup is filled to a depth of 8cm, that is 2/3 the full depth, so the radius of the water in the cup will be 2/3 of the full radius, which is 8/3cm. The volume of water is then

Since the question asks for an answer as the nearest whole number, perform the calculation and round as required.

Note that, though the problem gives a hint about using similar triangles, there is a much faster way to answer this question. If the height of the water in the cup is 2/3 the full height of the cup, then the volume of water in the cup is (2/3)^3 of the total volume:

b. This question is answered far more easily using the concept noted above.

If the volume is 1/2 of the total volume, then the height of the cone (depth of the water) is the full height, multiplied by the CUBE ROOT of 1/2.

to 4 decimal places.

Than round as directed.
RELATED QUESTIONS
A paper cup in the shape of a cone has a base diameter of 3 inches and a height of 4... (answered by checkley77)

A paper drinking cup in the shape of a right circular cone is constructed from 125 square (answered by Boreal)

A paper drinking cup in the shape of a cone has a height of 10 cm and a diameter of 8... (answered by macston)

If all the ice melted in the cup, would it overflow? A snowcone with a radius of 4 cm... (answered by josgarithmetic,MathTherapy,Alan3354)

A paper drinking cup is in the shape of a cone. The angle at the bottom of the cone is... (answered by Alan3354)

A store sells ice cream either in biscuit cones with diameter 6 centimeters and height H... (answered by josgarithmetic)

A paper cone of circular base diameter 10cm and height 12cm, is flattened out into the... (answered by ikleyn)

A snowcone with a radius of 4 cm is sold in a cone-shaped paper cup with a height of 12... (answered by math_tutor2020)

the volume of a paper cup, shaped like a circular cone, is 28pi cubic centimeters. The... (answered by Alan3354)