Question

In the diagram below, the surface area of the con is 100pi.. What is the height of the cone?

Answer 1

well is it : total surface area or curved one?

Answer 2

total

Answer 3

its asking for the height

Answer 4

You first need to find the value of r

Answer 5

So you must start with the surface area of a cone formula


SA = pi*r^2 + pi*r*s


where


r = radius

s = slant height


In this case,


s = 3r


Plug all this in to get


SA = pi*r^2 + pi*r*s


SA = pi*r^2 + pi*r*3r


SA = pi*r^2 + 3pi*r^2


SA = 4pi*r^2


Now plug in the given surface area to get


100pi = 4pi*r^2


and solve for r

Answer 6

r=5

Answer 7

now you can use that to find s

s = 3r

s = 3*5

s = 15

Answer 8

if you take a cross section of the cone, you get this triangle

Answer 9

but on my paper, it says the answer is 10 square root of 2

Answer 10

i know, we're not done yet

Answer 11

now focus on one right triangle to get this

Answer 12

we just found

r = 5 and s = 15

Answer 13

now solve

a^2 + b^2 = c^2

h^2 + 5^2 = 15^2

for h

Answer 14

?

Answer 15

yes, you'll have to show how to get that, but you are correct

Answer 16

factor tree . thank you much. i'm a straight A student, and i swear, i learned more from you than my teacher.

Answer 17

glad to be of help to you

Answer 18

Please help me with another question !

Answer 19

alright, what is it

Answer 20

The pyramid in the diagram is a regular pyramid and the base of the pyramid is a square. If the volume of the pyramid is 72cm^3, find the surface area of the pyramid.