Answer:
The radius of the cone is approximately 1.4 feet
Step-by-step explanation:
The given parameters of the cone are;
The height of the cone, h = 4 ft.
The volume of the cone, V = 7.77 ft.³
The volume, 'V', of a cone is given by the following formula;
V = 1/3 × π·r²·h
Where;
V = The volume of the cone = 7.77 ft.³
r = The radius of the cone
h = The height of the cone = 4 ft.
By substituting the vales of 'h' and 'V' in the above equation, we have;
7.77 ft.³ = 1/3 × π × r² × 4 ft.
∴ r = √(3 × 7.77 ft.³/(π × 4 ft.)) = 1.36196580784 ft.
∴ The radius of the cone, r ≈ 1.4 ft. (rounding the answer to the nearest 10th)
and 
. Then
(the part of the sphere above the cone) is given by