Question

The figure is made up of a hemisphere and a cylinder.

Answer 1

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
$\boxed{\boxed{Volume\:of\:the\:figure = 1517.6\:cm^3}}\end{array}}\qquad\quad\checkmark$

Answer 2

283 1/3 pi

The figure is made up of a hemisphere and a cylinder.

What is the exact volume of the figure?

Enter your answer in the box.  283 1/3 pi

I hope this helps