Question

A cone of height 9cm has a volume of ncm³ curved surface area of ncm². Find the vertical angle of the cone

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Answer 1

Explanation:

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