Hello, acc100jt!

This is how I did part (a) . . .

The side view of the cone looks like this: Code:

r
* - - + - - *
\ | /
\ | /
\ |h / R
\ | /
\|/
*

is the radius of the cone, is the height of the cone.

The slant height of the cone is: . .**[1]**

Since the volume is 100 cm³: .

Substitute into [1]: .

. . Hence: . .**[2]**

The cone is formed from a sector of the circle

. . with radius and central angle . Code:

* * *
* *
* *
* *
* *
* * *
* * θ * *
* * R
* * * *
* *
* *
* * *
Rθ

The area of the sector is: . .**[3]**

The arclength of the sector ,

. . is the circumference of the base of the cone .

Hence: .

Substitute into [3]: . .**[4]**

Substitute [2] into [4]: .

Therefore: .