Data: (Cylinder)
h (height) = 8 cm
r (radius) = 5 cm
Adopting: \(\pi \approx 3.14\)
V (volume) = ?
Solving:(Cylinder volume)
\(V = h* \pi *r^2\)
\(V = 8*3.14*5^2\)
\(V = 8*3.14*25\)
\(\boxed{ V_{cylinder} = 628\:cm^3}\)
Note: Now, let's find the volume of a hemisphere.
Data: (hemisphere volume)
V (volume) = ?
r (radius) = 5 cm
Adopting: \(\pi \approx 3.14\)
If: We know that the volume of a sphere is \(V = 4 * \pi * \frac{r^3}{3}\), but we have a hemisphere, so the formula will be half the volume of the hemisphere \(V = \frac{1}{2} * 4 * \pi * \frac{r^3}{3}\)
Formula: (Volume of the hemisphere)
\(V = \frac{1}{2} * 4 * \pi * \frac{r^3}{3}\)
Solving:
\(V = \frac{1}{2} * 4 * \pi * \frac{r^3}{3}\)
\(V = \frac{1}{2} * 4 * 3.14 * \frac{5^3}{3}\)
\(V = \frac{1}{2} * 4 * 3.14 * \frac{125}{3}\)
\(V = \frac{1570}{6}\)
\(\boxed{V_{hemisphere}\approx 261.6\:cm^3}\)
Now, to find the total volume of the figure, add the values: (cylinder volume + hemisphere volume)
Volume of the figure = cylinder volume + hemisphere volume
Volume of the figure = 628 cm³ + 261.6 cm³
\(\boxed{\boxed{Volume\:of\:the\:figure = 1517.6\:cm^3}}\end{array}}\qquad\quad\checkmark\)
