Question

Trigonometry question see pic in comments

Answer 1

if you cant read it The diagram s show a sector of radius 10cm and angle @ radians which is formed into a cone slant height of 10 cm. the verticle height h of the cone is equal to the radius r of its base. Find the angle @ radians

Answer 2

Do you know how to find the surface area of the cone?
It (not counting its bottom) must match the area of the part of the circle used to make the cone.

Answer 3

no, can you explain?

Answer 4

try google to find the surface area of a cone, and post the formula

Answer 5

\[\pi rs +\pi r ^{2}\]

Answer 6

the second part is the bottom of the cone. It does not count. The first term
pi * r *s is the part formed by the circle.
you know s (the slant height) see your picture.
you know height of the cone equals the radius, so you can figure out what r is
(45-45-90 triangle)

Answer 7

yes i found the surface area as 379 cm^2

Answer 8

the area of the circle is pi r^2 = 100 pi
now find the fraction theta/2*pi that matches the cone.

Answer 9

as in theta/2pi = 100 pi ?

Answer 10

no.
as in
\[ 100 \pi \frac{\theta}{2 \pi} = \text{area of cone} \]

Answer 11

btw, double check your answer for the area of the cone's top surface. I got 222.14

Answer 12

πrs+πr2, isnt that the formula for surface area of a cone? πrs = 222.14

Answer 13

yes, but the pi r^2 is not part of the circle. It is the bottom of the cone, which is open in this case. Look at the picture, or go fold a piece of paper to get an idea of what is happening.

Answer 14

oh right, thanks :)

Answer 15

btw, lots of times people would leave the answer as
\[ \theta= \sqrt{2} \pi \]
rather than
theta = 4.443 (rounded)

Answer 16

how did you get that answer? It is right but I dont understand the last steps

Answer 17

First, what is the area of the cone without simplifying to a single number.

Answer 18

222.11

Answer 19

no, pi *r*s with out simplifying

Answer 20

pi 7.07 x 10

Answer 21

what is 7.07 before you simplify?

Answer 22

oh ok, sq root 50

Answer 23

\[\pi \sqrt{50} \times 10\]

Answer 24

now we can simplify it this way
50= 25*2 so sqrt(50)= sqrt(25)*sqrt(2)= 5*sqrt(2)
we get
\[ \pi 50 \sqrt{2} \]
that is an exact result (remember 7.07 is only approximately sqrt(50))

now we solve the equation
\[ 100 \pi \frac{\theta}{2 \pi} = \pi 50 \sqrt{2} \]

Answer 25

the left hand side is the area of the circle (pi r^2 with r=10)
but we only want a fraction of the whole area. 2 pi is the whole way round
theta is part way round. theta/2pi is a fraction of the circle...does that make sense?

Answer 26

Yes thank you so much, I get it now :D