Question

A drinking glass is shaped like a cylinder with a height of 5 in. and a diameter of 3 in. Maeva adds 25 spherical pieces of ice to the glass. The pieces of ice each have a diameter of 1.1 in.

How many cubic inches of water can Maeva add to fill the glass to the rim? Use 3.14 to approximate pi and round your answer to one decimal place.

_____ in3

Answer 1

Do you know the formula for the volume of a cylinder ?

Answer 2

no.

Answer 3

@phi

Answer 4

Do you have notes?
Here is the formula
http://www.mathopenref.com/conevolume.html

you also need the formula for the volume of a cylinder
http://www.mathopenref.com/cylindervolume.html

Answer 5

ok.

Answer 6

no, wait, we need the formula for sphere (not cone)
http://www.mathopenref.com/spherevolume.html

Answer 7

the first step is use the formula to find the volume of the cylinder
a cylinder with a height of 5 in. and a diameter of 3 in.
(diameter 3 inches means radius is 1.5 inches)

can yo find the volume ? using V= pi r^2 h

Answer 8

oh. i was kinda confused when i looked at that.

Answer 9

by V= pi r^2 h ?

Answer 10

no. because it was the wrong formula

Answer 11

sorry about the cone. But the formula for the cylinder is
V= pi r^2 h

can you use it, with pi= 3.14, r= 1.5 and h=5 ?

Answer 12

its ok.

Answer 13

can you find the volume for the cylinder?

Answer 14

i think. im doing so now.

Answer 15

i did, but i got a weird number. 1354721.23348033

Answer 16

@phi is that the answer?

Answer 17

that is definitely wrong. what did you do
the formula
V= pi r^2 h
means : replace pi with 3.14. for this problem replace r with 1.5 and h with 5
and do the arithmetic
3.14 * (1.5)^2 * 5
remember order of operations? do 1.5^2 first (which means 1.5*1.5 )
then multiply by 3.14
then multiply by 5

Answer 18

35.325

Answer 19

next, we put in 25 spheres into the cylinder (and they will use up some of the space)
(think putting marbles into a glass)

each sphere will take up some amount of volume. \( = \frac{4}{3} \pi r^3 \)

you should replace r with the radius of the sphere. You know the diameter is 1.1 inches, and the radius will be one-half of this diameter

Answer 20

Yes 35.325 is the volume of the cylinder.
Now you need to find the volume of 1 sphere, and then multiply by 25 (because you have 25 spheres)
can you do that ?

Answer 21

to find the volume of one sphere, first figure out its radius
its diameter is 1.1. Its radius is 1/2 of the diameter, so 1/2 *1.1 = ??

Answer 22

i think i am going with my answer. i rounded it and everything

Answer 23

0.55