A cone-shaped glass and a tin can are filled with water. The height of the cone is 12" (12 inches) and it has a radius of 1.5" (1½ inches). The can is 2 inches high and has a diameter of 4 inches. Which container holds more water? How much more water does the larger container hold? Use 3.14 for π, and remember to use the correct units in your answer.
Explain how you solved this problem, and name any rules or theorems you used. Show all your work.
cone = (1/3)π r^2 h
where r = 1.5
h = 12
find the volume of the cone, just plug in the values
Can = π r^2 h
r = 2
h = 2
volume of can = .....
compare to see which is larger.
take the difference to see which hold more
25.13 volume of a can with 2 and 2
To solve this problem, we need to compare the volumes of the cone-shaped glass and the tin can. We can use the formulas for the volume of a cone and the volume of a cylinder to find the volumes of the two containers.
The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, π is approximately 3.14, r is the radius, and h is the height.
The formula for the volume of a cylinder is V = πr^2h, where V is the volume, π is approximately 3.14, r is the radius, and h is the height.
Let's calculate the volume of the cone-shaped glass first:
V_cone = (1/3) * 3.14 * (1.5^2) * 12
V_cone = (1/3) * 3.14 * 2.25 * 12
V_cone = 3.14 * 2.25 * 4
V_cone = 28.26 cubic inches
Now let's calculate the volume of the tin can:
V_can = 3.14 * (2^2) * 2
V_can = 3.14 * 4 * 2
V_can = 25.12 cubic inches
Now we can compare the volumes of the two containers. The cone-shaped glass has a volume of 28.26 cubic inches, while the tin can has a volume of 25.12 cubic inches.
To find how much more water the larger container holds, we subtract the volume of the smaller container from the volume of the larger container:
Difference = V_cone - V_can
Difference = 28.26 - 25.12
Difference = 3.14 cubic inches
Therefore, the cone-shaped glass holds 3.14 cubic inches more water than the tin can.
In this problem, we used the formulas for the volume of a cone and the volume of a cylinder, as well as the properties of circles (such as radius and diameter). We also used the concept of subtracting one volume from another to find the difference.