Question

a half - cylinder has diameter 35 cm and height 70 cm. determine the volume of the half - cylinder.
a) about 269392 cm³
b) about 33674 cm³
c) about 67348 cm³
d) about 134696 cm³

Explanation:

Step1: Find the radius

The diameter $d = 35$ cm, so the radius $r=\frac{d}{2}=\frac{35}{2}$ cm.

Step2: Recall the volume formula for a half - cylinder

The volume formula for a full cylinder is $V=\pi r^{2}h$. For a half - cylinder, $V_{half}=\frac{1}{2}\pi r^{2}h$.

Step3: Substitute the values of $r$ and $h$

We have $r = \frac{35}{2}$ cm and $h = 70$ cm. Substitute into the formula:
\[

$$\begin{align*} V_{half}&=\frac{1}{2}\times\pi\times(\frac{35}{2})^{2}\times70\\ &=\frac{1}{2}\times\pi\times\frac{35^{2}}{4}\times70\\ &=\frac{1}{2}\times\pi\times\frac{1225}{4}\times70\\ &=\frac{1\times\pi\times1225\times70}{2\times4}\\ &=\frac{85750\pi}{8}\\ &\approx\frac{85750\times3.14}{8}\\ &=\frac{269255}{8}\\ & = 33656.875\approx33674\text{ cm}^3 \end{align*}$$

\]

Answer:

b) About 33 674 cm³