Question
one glass cylinder and one glass cone with the same height and radius
if the height of the glass doubled and then the volumes would increase times ___
(use for formulas to substitute V=1/3πr^2h and V=πr^2h)
if the height of the glass doubled and then the volumes would increase times ___
(use for formulas to substitute V=1/3πr^2h and V=πr^2h)
Answers
GPT 3.5
First, let's calculate the initial volume of the glass cone and the glass cylinder.
Given that the height and radius of both shapes are the same:
- Volume of the cone (V_cone) = (1/3) * π * r^2 * h
- Volume of the cylinder (V_cylinder) = π * r^2 * h
Since the height and radius are the same for both shapes, let's just use the variable r for the radius and h for the height:
V_cone = (1/3) * π * r^2 * h
V_cylinder = π * r^2 * h
Now, let's calculate the new volume of the glass cone and cylinder when the height is doubled:
New height (2h):
- Volume of the new cone = (1/3) * π * r^2 * 2h
- Volume of the new cylinder = π * r^2 * 2h
Now, let's calculate the increase in volume for both shapes when the height is doubled:
Increase in volume for the cone = (1/3) * π * r^2 * 2h / ((1/3) * π * r^2 * h)
Increase in volume for the cylinder = π * r^2 * 2h / (π * r^2 * h)
Simplify these expressions:
Increase in volume for the cone = 2
Increase in volume for the cylinder = 2
Therefore, when the height of the glass cone and cylinder is doubled, their volumes will increase by a factor of 2.
Given that the height and radius of both shapes are the same:
- Volume of the cone (V_cone) = (1/3) * π * r^2 * h
- Volume of the cylinder (V_cylinder) = π * r^2 * h
Since the height and radius are the same for both shapes, let's just use the variable r for the radius and h for the height:
V_cone = (1/3) * π * r^2 * h
V_cylinder = π * r^2 * h
Now, let's calculate the new volume of the glass cone and cylinder when the height is doubled:
New height (2h):
- Volume of the new cone = (1/3) * π * r^2 * 2h
- Volume of the new cylinder = π * r^2 * 2h
Now, let's calculate the increase in volume for both shapes when the height is doubled:
Increase in volume for the cone = (1/3) * π * r^2 * 2h / ((1/3) * π * r^2 * h)
Increase in volume for the cylinder = π * r^2 * 2h / (π * r^2 * h)
Simplify these expressions:
Increase in volume for the cone = 2
Increase in volume for the cylinder = 2
Therefore, when the height of the glass cone and cylinder is doubled, their volumes will increase by a factor of 2.
Related Questions
there is a glass cylinder and a glass cone with the same height and radius
If the height of the gla...
there is a glass cylinder and a glass cone with the same height and radius
If the height and radiu...
one glass cylinder and one glass cone with the same height and radius
if the radius of the glass d...
one glass cylinder and one glass cone with the same height and radius
if the radius and the height...