Question

Find the total volume of the following composite figure with

h=4.3

and

r=3.9

Use 3.14 for LaTeX: \piπ.

Round to the nearest hundredth.

Answer 1

Given:

A composite figure consisting of a cylinder with radius r and height h and a half-sphere with a radius r.

To find:

The total volume of the composite figure.

Solution:

To determine the total volume of the figure, we add the volume of the cylinder and the volume of the half-sphere.

The volume of a cylinder,
`V= \pi r^(2) h.`

The given cylinder has a radius of 3.9 units and a height of 4.3 units. Assume π equals 3.14.

The volume of the cylinder,
`V = (3.14)(3.9^(2) )(4.3)= 205.36542` cubic units.

The volume of a half-sphere,
`V= (2)/(3) \pi r^(3) .`

The given half-sphere has a radius of 3.9 units, assume π equals 3.14.

The volume of the half-sphere,
`V= (2)/(3) (3.14)(3.9^(3) ) = 124.17444` cubic units.

The total volume of the composite figure
`= 205.36542+124.17444=329.53986` cubic units.

Rounding this off to the nearest hundredth, we get the volume of the cone as 329.54 cubic units.