14. A right cone has a height of 14 in and a base diameter of 17 in.
a Sketch and label a diagram of the cone
b. Determine the area of the lateral surface of the cone, to the nearest square inch
Answers
Given:
The height of a right cone = 14 in
Base diameter = 17 in
To find:
The diagram of the cone and its lateral surface area.
Solution:
(a)
The diagram of a right cone with height 14 in and base diameter of 17 in is shown below.
Diagram is not to scale.
(b)
We know that lateral surface of the cone is
[tex]A=\pi rl[/tex]
[tex]A=\pi r\sqrt{r^2+h^2}[/tex] ...(i)
Where, r is the base radius, h is vertical height and l is the slant height of the cone.
Base radius of the cone = [tex]\dfrac{\text{Base diameter}}{2}[/tex]
[tex]r=\dfrac{17}{2}[/tex]
[tex]r=8.5[/tex]
Now,
Putting r=8.5, h=14 and π=3.14 in (i), we get
[tex]A=(3.14)(8.5)\sqrt{(8.5)^2+(14)^2}[/tex]
[tex]A=26.69\sqrt{72.25+196}[/tex]
[tex]A=26.69\sqrt{268.25}[/tex]
[tex]A=437.1379[/tex]
[tex]A\approx 437[/tex]
Therefore, the lateral surface area of the cone is 437 sq. inches.
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