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