A cone height is 9cm has a volume of n cm3 and a curved surface area of ncm2. Find the vertical angle of the cone
h=9cm, v=n cm^3, c.s.a=n cm^2. Volume of cone is 1/3*22/7*r^2*h, therefore n=1/3*22/7*r^2*9=66r^2/7 therefore n=66r^2/7 now cross multiply 7n=66r^2 b.b.s by 66 we get r^2=7n/66 therefore r=√7n divided by √66. Also c.s.a=πrl therefore n=22/7*√7n divided by √66*l.then we have 22l*√7n* √66*7=n. Cross multiply, we have 22l *√7n=n*7√66 d. b.s by 22√7n=7n√66/22√7n.
When you have a cone, in order to find vertical angle, divide the cone into two. We then have two right angled triangles. Let the missing angle be represented with @. Now using sin@=r/l. There4 sin@=√7n/√66÷7n√66/22√7n=√7n/√66*22√7n/7n√66=154n÷7n*66=154n*1/7n*66=22/66. Therefore sin@=22/66= 0.333. Therefore sin@=0.333.@=sin–¹0.333=19.45.vertical angle=2@=2*19.45=38.9
The answer in my text book is 38.9degrees
I checked the answers in my textbook and I got to know that the answer to this question was 38.9 degree instead of the answer chrome gave me
That is what they wrote in my textbook 38.9°
Pls help me to solve it now
Thanks you saved me from Mr isa
Too complicated
What question
It seems that you have resolved your previous question. Do you have any other questions?
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°
check my arithmetic
I do get it
The person that solved it should snap it so as to make it more understandable