A mass of cylinder m varies jointly as the square of the radius and as the height h.If the radius is increased by 20% and the height by 10%,find the percentage increase in mass
Let's assume that the mass of the cylinder is given by the equation: m = k * r^2 * h, where k is the constant of variation.
If we increase the radius by 20%, the new radius becomes 1.2r.
Similarly, if we increase the height by 10%, the new height becomes 1.1h.
Therefore, the new mass (m') of the cylinder can be calculated as follows:
m' = k * (1.2r)^2 * (1.1h)
= k * 1.44 * r^2 * 1.21 * h
= (1.44 * 1.21) * (k * r^2 * h)
= 1.74 * m
So, the new mass (m') is 1.74 times the original mass (m).
To find the percentage increase in mass, we can use the formula:
% Increase = ((new mass - original mass) / original mass) * 100
Plugging in the values, we get:
% Increase = ((1.74m - m) / m) * 100
= (0.74m / m) * 100
= 74%
Therefore, the percentage increase in mass is 74%.
To solve this problem, let's assume the initial mass is M, the initial radius is R, and the initial height is H.
According to the problem, the mass of the cylinder varies jointly as the square of the radius and as the height. Mathematically, we can express this relationship as:
M ∝ R^2 * H
Now, let's consider the new values after the radius and height are increased. The new radius is 1.2R (20% increase), and the new height is 1.1H (10% increase). Let's denote the new mass as M'.
Using the relationship stated earlier, the new mass can be expressed as:
M' ∝ (1.2R)^2 * (1.1H)
∝ 1.44R^2 * 1.1H
∝ 1.584R^2 * H
Now, we want to find the percentage increase in mass, which can be calculated as:
Percentage increase = [(M' - M) / M] * 100
Substituting the values of M and M' into the equation:
Percentage increase = [(1.584R^2 * H - M) / M] * 100
However, without knowing the specific values of R and H, we cannot calculate the exact percentage increase in mass. You would need to provide the specific values of the radius and height in order to proceed with the calculation.