Question

Find the volume of the composite solid shown. Round to the nearest tenth.

Answer 1

Answer:

113.1 $cm^{3}$

Step-by-step explanation:

The equation to find the volume of a cylinder is:

$V = \pi r^{2} h$

V = volume

r = radius

h = height

The radius of the cylinder is 3 in, and the height of the cylinder is 2 in. Plug these into the equation:

$V = \pi (3)^{2} (2)$

Solve (use calculator):

V = $18\pi$ or 56.55 $cm^{3}$

To find the volume of the half sphere use this equation:

$V = \frac{1}{2}(\frac{4}{3} \pi r^{3} )$

The radius of the circle is 3 in, plug this into the equation:

$V=\frac{1}{2} (\frac{4}{3} \pi (3^{3}))$

Solve (use calculator):

V = $18\pi$ or 56.55 $cm^{3}$

To find the volume of the entire shape just add the separate volumes together:

V( of cylinder) + V( of sphere) = Total volume

$56.55 cm^{3}+56.55 cm^{3}= 113.1 cm^{3}$

Or, you could rewrite this as 36$\pi$

So, the answer is that the volume of the composite solid is 113.1 $cm^{3}$