Question

Your friend brings hot chocolate to school in the cylindrical thermos and drinks from her cylindrical mug shown.

1. Your friend fills the thermos with hot chocolate to a height of 10 inches. How much does she bring to school? Leave your answer in terms of π.


2. The inside bottom of the mug is 4 inches from the top. Find the volume of the mug. Leave your answer in terms of π. 3(π)in^3?


3. Each time your friend fills the mug, she fills it 80% full and then drinks it completely before filling up again. How much hot chocolate does she pour into the mug each time? Leave your answer in terms of π.


4. Is the mug more than half full after the last pour from the thermos? Justify your answer.

Answer 1

volume=height times area of base
base=circle so area of base=pir^2
ok so solume=height times pi times r^2


1.
thermos, h=10, r=2
therefor
 volume=10pi2^2=
 volume=10pi4=
40pi in^3 is brought to school


2. inside is 4 inches deep
h=4, r=1.5
volume=4pi1.5^2
volume=4pi2.25
volume=9pi
answer is 9pi in^3


3. so find 80% of 9pi
80%=0.8
0.8 times 9pi=7.2pi in^3
each times is 7.2pi in^3


4. ok so this is assuming that you fill the mug to 80% (7.2pi) each time and the remainder is it less or more or equal to half of 7.2pi so

total in thermos=40pi
each pour=7.2pi
40pi-7.2pi-7.2pi-7.2pi-7.2pi-7.2pi=4pi
is 4pi more or less than 7.2pi
7.2pi/2=3.6pi
4pi>3.6pi
it is MORE


1. 40pi in^3
2. 9pi in^3
3. 7.2pi in^3
4. MORE than half