Question

A cone of height 9cm has a volume of n cm3 and a curved surface area of n cm2. Find the vertical angle of the cone

Answer 1

let the radius be r and the slant height be L
then first of all: L^2 = r^2 + 9^2
= r^2 + 81

Surface area = πrL = n
volume = (1/3)πr^2 (9) = 3πr^2 = n

then 3πr^2 = πrL
3r = L , then in L^2 = r^2 + 81
9r^2 = r^2 + 81

8r^2 = 81
r = 9/√8
L^2 = 81/8 + 81 = 729/8
L = √1458/4
cos(baseangle) = (9/√8) / (√1458/4)
= 1/3
angle of base = appr 70.5°

Answer 2

I agree, I got the same

Answer 3

The answer is 38.9.
I don't understand how you did it.

Answer 4

I don't understand how you did it

Answer 5

I don't understand how you did it

Answer 6

What is the formular for finding verticle angle of the cone

Answer 7

ncm³=ncm²
⅓πr²h=πrl
⅓πr²9=πrl
⅓πr²9/πr=πrl/πr
9r/3=l
Cross multiply
9r=3l
r=3l/9
r=⅓l
Divide both sides by l
r/l=⅓
r/l=0.3333=sin°
Sin-1°=19.471
Vertical angle=2(°)
2(°)=2(19.471)
2(°)=38.94
…Vertical angle=38.9(to 0.1°)

Answer 8

ino get

Answer 9

how was the square root of 1458/4 gotten