The volume of a cone is 180cm^3 , if the radius and the height are 3 times more, what would be the volume ???
given 1/3 PI r^2 * h=180
then 1/3 PI (3r)^2*(3h)=?
1/2 pi r^2 h * 27=27*180
So would the answer be 4,860 ??
To find the new volume of the cone when the radius and height are three times more, we need to calculate the new values for the radius and height.
Let's assume the original radius of the cone is 'r' and the original height is 'h'.
Given that the volume of the cone is 180 cm³, we can use the formula for the volume of a cone, which is V = (1/3) * π * r² * h.
Substituting the given values, we have:
180 = (1/3) * π * r² * h
To simplify the calculation, we can cancel out the (1/3) factor by multiplying both sides of the equation by 3:
3 * 180 = π * r² * h
Since π is a constant value, we can rearrange the equation to isolate r² * h:
r² * h = (3 * 180) / π
Now, if the radius and height are three times more, we multiply both r and h by 3. Therefore, the new radius and new height are 3r and 3h respectively:
(new radius)² * (new height) = (3r)² * (3h)
= 9 * r² * 9 * h
= 81 * r² * h
So, the new volume, expressed in terms of the original volume, can be found by multiplying the original volume by 81:
(new volume) = (original volume) * 81
= 180 * 81
= 14,580 cm³
Therefore, the new volume of the cone, when the radius and height are three times more, would be 14,580 cm³.