Question

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​

Answer 1

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

$A=\pi rl$

$A=\pi r\sqrt{r^2+h^2}$              ...(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 = $\dfrac{\text{Base diameter}}{2}$

$r=\dfrac{17}{2}$

$r=8.5$

Now,

Putting r=8.5, h=14 and π=3.14 in (i), we get

$A=(3.14)(8.5)\sqrt{(8.5)^2+(14)^2}$

$A=26.69\sqrt{72.25+196}$

$A=26.69\sqrt{268.25}$

$A=437.1379$

$A\approx 437$

Therefore, the lateral surface area of the cone is 437 sq. inches.