Question

1. the formula for the volume of a cylinder is $v = \pi r^{2}h$. determine the volume of the cylinder shown below, rounded to the nearest cubic centimetre.

diagram not drawn to scale
a. $1257\\ cm^{3}$
b. $251\\ cm^{3}$
c. $1005\\ cm^{3}$
d. $503\\ cm^{3}$

Explanation:

Step1: Identify the values of \(r\) and \(h\)

From the diagram, the radius \(r = 8\) cm and the height \(h=10\) cm.

Step2: Substitute into the volume formula

Substitute \(r = 8\) and \(h = 10\) into \(V=\pi r^{2}h\). So \(V=\pi\times(8)^{2}\times10\).
First, calculate \((8)^{2}=64\). Then \(V=\pi\times64\times 10=640\pi\).

Step3: Calculate the numerical value

Using \(\pi\approx3.14159\), \(V = 640\times3.14159\approx2010.6176\). Wait, no, there's a mistake. Wait, no - wait the formula is \(V=\pi r^{2}h\). Wait, hold on, no - wait the radius is \(r = 8\) (radius is from center to the side, if the line shown is radius). Wait no - wait the formula \(V=\pi r^{2}h\). If \(r = 8\) (radius) and \(h=10\). But wait, no - wait maybe mis - look. Wait no, hold on. Wait the formula \(V=\pi r^{2}h\). If \(r = 8\) (radius) and \(h = 10\). But wait, no - wait the options. Wait hold on, no - wait maybe the radius is \(r = 4\) (if the given \(8\) is diameter). Wait the problem says "the formula for the volume of a cylinder is \(V=\pi r^{2}h\). Determine the volume...". If the diagram has a line labeled \(8\) cm - if that's the diameter (since in a cylinder, if it's from one side through the center to the other, that's diameter). So \(r=\frac{d}{2}=\frac{8}{2} = 4\) cm, \(h = 10\) cm.
Now substitute \(r = 4\) and \(h=10\) into \(V=\pi r^{2}h\). \(V=\pi\times(4)^{2}\times10\).
Calculate \((4)^{2}=16\). Then \(V=\pi\times16\times10 = 160\pi\).
Using \(\pi\approx3.14159\), \(V=160\times3.14159 = 502.6544\approx503\) \(cm^{3}\).

Answer:

d. \(503\ cm^{3}\)