A cone with a radius of 3 cm, and a volume of 900cm.
The height is 95.493cm?
how is the volume affected if the height is doubled, and how is it affected if the radius is doubled?
Are these correct?
After doubled height:
The volume is doubled
Volume after doubled height: 1800cm
After doubled radius:
The volume is quadrupled
Volume after doubled radius: 3600cm
V = (1/3)πr^2 h
so if you just double the height, the volume is doubled
if you double the radius, the volume will be quadrupled
r^2 ----> (2r)^2 = 4r^2
if you double both height AND radius, the volume would increase
by a factor of 8
r^2 h ---> (2r)^2 (2h) = 8r^2 h
To determine how the volume of a cone is affected when either the height or the radius is doubled, we need to understand the formula for calculating the volume of a cone and then apply the changes to the respective measurements.
The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the cone's base, and h is the height of the cone.
Let's start with the original cone with a radius of 3 cm and a height of 95.493 cm. Given that the volume is 900 cm^3, we can set up the equation as follows:
900 cm^3 = (1/3)π(3 cm)^2(95.493 cm)
Now, to examine how the volume is affected if the height is doubled, we can calculate the new volume using the doubled height of 2 * 95.493 cm = 190.986 cm:
V_new = (1/3)π(3 cm)^2(190.986 cm)
Similarly, to examine how the volume is affected if the radius is doubled, we can calculate the new volume using the doubled radius of 2 * 3 cm = 6 cm:
V_new = (1/3)π(6 cm)^2(95.493 cm)
By comparing the new volumes to the original volume, we can determine how the changes in height and radius affect the volume of the cone.