If the diameter of a sphere is increase by 20% the volume also increased by x% find x??
if the diameter scales by a factor of x, the volume grows by x^3.
So, if d -> 1.2d
v -> 1.2^3 v = 1.728v
That is, it grows by 72.8%
How did u got 72.8% but i get what your are saying tnx
I don't think Steve is on line right now, so ...
look at his
1.728v
= (1 + .728)v
= (100% + 72.8%)v , since 100% = 100/100 = 1
can you see where it came from?
Tnx reiny........bess yah
Dang it, buddy, you're taking all the mystery out of math!
What happen steve why??
Let the diameter be 100cm
Then,its volume=(4/3)π50³
When diameter increased by 20%,diameter becomes 120cm
Then its volume =(4/3)π60³
%increase in volume=
{[(4/3)π60³-(4/3)π50³]/(4/3)π50³}X100
=(21600000-12500000)/125000
=72.8%
yea nah don't get it
To find the percentage increase in volume when the diameter of a sphere is increased by 20%, we need to understand the relationship between the diameter and volume of a sphere.
The volume of a sphere is given by the formula:
V = (4/3) * π * r^3,
where V is the volume and r is the radius of the sphere.
Since the diameter is twice the length of the radius, we can relate them as follows:
d = 2r,
where d is the diameter and r is the radius.
Now, let's consider the increase in diameter. If the initial diameter is d, and we increase it by 20%, the new diameter would be:
new_d = d + (20/100) * d = 1.2d.
Using the relationship between diameter and radius, the new radius would be:
new_r = (1/2) * new_d = (1/2) * 1.2d = 0.6d.
Now, let's calculate the new volume of the sphere:
new_V = (4/3) * π * (new_r)^3 = (4/3) * π * (0.6d)^3.
To find the percentage increase in volume, we need to compare the new volume (new_V) with the initial volume (V) and calculate the difference. The percentage increase is given by:
x = (new_V - V) / V * 100%.
Substituting the values, we get:
x = [(4/3) * π * (0.6d)^3 - (4/3) * π * r^3] / [(4/3) * π * r^3] * 100%.
Simplifying further, we can cancel out some terms:
x = [(0.6d)^3 - r^3] / r^3 * 100%.
x = [0.216d^3 - r^3] / r^3 * 100%.
Since we know that d = 2r, we can substitute this value into the equation:
x = [0.216(2r)^3 - r^3] / r^3 * 100%.
x = [0.216 * 8r^3 - r^3] / r^3 * 100%.
x = [1.728r^3 - r^3] / r^3 * 100%.
x = 0.728r^3 / r^3 * 100%.
Simplifying further, we find:
x = 0.728 * 100%.
Therefore, x = 72.8%.
Hence, the volume increases by 72.8% when the diameter of a sphere is increased by 20%.