Question

Find the lateral surface area and the volume of the figure in picture(Round to the nearest integer as needed)

Answer 1

The total surface area of a cone is the following;

`SA=\pi r^2+\pi\cdot r\cdot l`

where:

r : radius

l : slant height

In this example:

r = 12''

l = 37''

therefore, SA

`SA=\pi\cdot(12)^2+\pi\cdot12\cdot37=1847.26`

rounding to the nearest integer; Total surface area: SA = 1847 in^2

The lateral surface area is given by:

`LA=\pi\cdot r\cdot l`

where:

r : radius = 12''

l : slant height = 37''

Then:

`LA=\pi\cdot12\cdot37=1394.87`

rounding to the nearest integer; Lateral surface area: LA = 1395 in^2

The volume of a cone is given by:

`V=\pi r^2\cdot(h)/(3)`

where:

r: radius = 12''

h: Height = 35''

So...

`V=\pi\cdot(12)^2\cdot(35)/(3)=5277.88`

rounding to the nearest integer; Volume: V = 5278 in^3