Question

please help me !! and explain !!

Answer 1

The volume of a cylinder is the base area times its height, which means

$V = \pi r^2\cdot h$

So, plugging the values from the second cylinder, we have

$88 = 4\pi\cdot h$

And solving for h we have

$h = \dfrac{88}{4\pi} = \dfrac{22}{\pi}$

Now, we know that cylinders A and B are similar, which means that corresponding parts are in the same proportions:

$r_a : r_b = h_a : h_b$

we know both radii, and the height of figure B, so we can solve for the height of figure A:

$h_a = \dfrac{r_ah_b}{r_b} = \dfrac{5\frac{22}{\pi}}{2} = \dfrac{55}{\pi}$

So, the volume of figure A is

$V = \pi r_a^2\cdot h_a = \pi \cdot 25 \cdot \dfrac{55}{\pi} = 25 \cdot 55 = 1375$

Note:

There is a shortcut for these kind of exercise. Once you know the constant of proportion, you can use it for areas and volumes as well. In this case, the rate of proportion is 5:2 (just compare the radii). So, the volume will scale with a factor of (5/2)^3, and we could simply have used

$V_a = 88 \cdot \left(\dfrac{5}{2}\right)^3 = 1375$