Question

the radius of a cylinder is tripled, and the height is halved. by what factor does the volume change?
a. 6
b. 4.5
c. 2
d. 1.5
a cylinder has a radius of 2.5 cm and a height of 10 cm. what is its approximate volume using π ≈ 3.14?
a. 200.50 cm³
b. 185.30 cm³
c. 196.25 cm³
d. 196.40 cm³

Explanation:

First Question

Step1: Recall volume formula

The volume formula of a cylinder is $V = \pi r^{2}h$. Let the original radius be $r$ and height be $h$, so the original volume $V_1=\pi r^{2}h$.

Step2: Calculate new - volume

The new radius is $3r$ and the new height is $\frac{h}{2}$. The new volume $V_2=\pi(3r)^{2}\times\frac{h}{2}=\pi\times9r^{2}\times\frac{h}{2}=\frac{9}{2}\pi r^{2}h$.

Step3: Find the change factor

To find the factor by which the volume changes, we calculate $\frac{V_2}{V_1}=\frac{\frac{9}{2}\pi r^{2}h}{\pi r^{2}h}=\frac{9}{2}=4.5$.

Step1: Apply volume formula

The volume formula of a cylinder is $V=\pi r^{2}h$. Given $r = 2.5$ cm and $h = 10$ cm, and $\pi\approx3.14$.

Step2: Substitute values

Substitute the values into the formula: $V\approx3.14\times(2.5)^{2}\times10$. First, calculate $(2.5)^{2}=6.25$. Then $V\approx3.14\times6.25\times10 = 3.14\times62.5=196.25$ $cm^{3}$.

Answer:

b. 4.5

Second Question